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20 September 2009, Volume 29 Issue 5 Previous Issue    Next Issue

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STRONG CONVERGENCE RATES OF SEVERAL  ESTIMATORS IN SEMIPARAMETRIC VARYING-COEFFICIENT PARTIALLY  LINEAR MODELS Zhou Yong；You Jinhong；Wang Xiaojing Acta mathematica scientia,Series B. 2009, 29 (5):  1113-1127.  DOI: 10.1016/S0252-9602(09)60090-4 Abstract ( 938 )   RICH HTML PDF (213KB) ( 1320 )   Save This article is concerned with the estimating problem of semiparametric varying-coefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang (2005) proposed a profile least squares estimator for the parametric component  and established its asymptotic normality.  We further show that the profile least squares estimator can achieve the  law of iterated logarithm. Moreover, we study the estimators of  the functions characterizing the non-linear part  as well as the error variance.  The strong convergence rate and the law of iterated logarithm   are derived  for them, respectively. References | Related Articles | Metrics

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METHOD OF CENTERS ALGORITHM FOR MULTI-OBJECTIVE PROGRAMMING PROBLEMS Tarek Emam Acta mathematica scientia,Series B. 2009, 29 (5):  1128-1142.  DOI: 10.1016/S0252-9602(09)60091-6 Abstract ( 828 )   RICH HTML PDF (192KB) ( 1650 )   Save In this paper, we consider a method of centers for solving multi-objective programming problems, where the objective functions involved are concave functions and the set of feasible points is convex. The algorithm is defined so that the sub-problems that must be solved during its execution may be solved by finite-step procedures. Conditions are given under which the algorithm generates sequences of feasible points and constraint multiplier vectors that have accumulation points satisfying the KKT conditions. Finally, we establish convergence of the proposed method of centers algorithm for solving multi-objective programming problems. References | Related Articles | Metrics

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BRUNN-MINKOWSKI INEQUALITY FOR VARIATIONAL FUNCTIONAL INVOLVING THE  P-LAPLACIAN OPERATOR HU Hua-Xiang, ZHOU Shu-Qing Acta mathematica scientia,Series B. 2009, 29 (5):  1143-1154.  DOI: 10.1016/S0252-9602(09)60092-8 Abstract ( 691 )   RICH HTML PDF (203KB) ( 1666 )   Save In this paper, we investigate the following elliptic problem involving the P-Laplacian  (P) {   -Div(| u|p-2    u) =|u|q-1u  in  K,   u>0                                    in  K,   u=0                                    on  ∂K, where p>1, 0<q<p-1, K     Rn with K ∈ Kn , and prove that the energy integral of the problem (P) satisfies a Brunn-Minkowski type inequality. References | Related Articles | Metrics

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LOCAL TIME ANALYSIS OF ADDITIVE L\'EVY PROCESSES WITH DIFFERENT LÉVY EXPONENTS ZHONG Yu-Quan Acta mathematica scientia,Series B. 2009, 29 (5):  1155-1164.  DOI: 10.1016/S0252-9602(09)60093-X Abstract ( 658 )   RICH HTML PDF (191KB) ( 1079 )   Save Let X1,…,XN be independent, classical Lévy processes on Rd with Lévy exponents Ψ1,…,ΨN, respectively. The corresponding  additive Lévy process is defined as the following $N$-parameter random field on Rd, X(t)=X1(t1)+…+XN(tN), ∨t ∈ RN+. Under mild regularity conditions on the Ψi's, we derive estimate for the local and uniform moduli of continuity of local times of X={X(t);t ∈ RN+}. References | Related Articles | Metrics

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EXISTENCE OF GLOBAL ATTRACTORS FOR A NONLINEAR EVOLUTION EQUATION IN SOBOLEV SPACE Hk ZHANG Yin-Di, LI Kai-Tai Acta mathematica scientia,Series B. 2009, 29 (5):  1165-1172.  DOI: 10.1016/S0252-9602(09)60094-1 Abstract ( 834 )   RICH HTML PDF (159KB) ( 1333 )   Save In this paper we prove that the initial-boundary value problem for the nonlinear evolution equation ut=Δu+λu-u3 possesses a global attractor in Sobolev space Hk for all k≥0, which attracts any bounded domain of Hk(Ω) in the Hk-norm. This result is established by using an iteration technique and regularity estimates for linear semigroup of operator, which extends the classical result from the case k∈ [0,1] to the case k∈ [0, ∞). References | Related Articles | Metrics

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ON THE CONVERGENCE OF CIRCLE PACKINGS TO THE QUASICONFORMAL MAP HUANG Xiao-Jun, CHEN Liang Acta mathematica scientia,Series B. 2009, 29 (5):  1173-1181.  DOI: 10.1016/S0252-9602(09)60095-3 Abstract ( 1194 )   RICH HTML PDF (189KB) ( 2033 )   Save Rodin and Sullivan (1987) proved Thurston's conjecture that a scheme based on the Circle Packing Theorem converges to the Riemann mapping, thereby proved a refreshing geometric view of the Riemann Mapping Theorem. Naturally, we consider to use the ellipses to pack the bounded simply connected domain and obtain similarly a sequence simplicial homeomorphism between the ellipse packing and the circle packing. In this paper, we prove that these simplicial homeomorphism approximate a quasiconformal mapping from the bounded simply connected domain onto the unit disk with the modulus of their complex dilatations tending to 1 almost everywhere in the domain when the ratio of the longer axis and shorter axis of the ellipse tending to ∞. References | Related Articles | Metrics

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NEW STRUCTURES FOR NON-SELFSIMILAR SOLUTIONS OF MULTI-DIMENSIONAL CONSERVATION LAWS YANG Xiao-Zhou, WEI Tao Acta mathematica scientia,Series B. 2009, 29 (5):  1182-1202.  DOI: 10.1016/S0252-9602(09)60096-5 Abstract ( 899 )   RICH HTML PDF (267KB) ( 1052 )   Save In this article, we get non-selfsimilar elementary waves of the conservation laws in another kind of view, which is different from the usual self-similar transformation. The solution has different global structure. This article is divided into three parts. The first part is introduction. In the second part, we discuss non-selfsimilar elementary waves and their interactions of a class of two-dimensional conservation laws. In this case, we consider the case that the initial discontinuity is parabola   with u+>0, while explicit non-selfsimilar rarefaction wave can be obtained. In the second part, we consider the solution structure of case u+<0. The new solution structures are obtained by the interactions between different elementary waves, and will  continue to interact with other states. Global solutions would be very different from the situation of  one dimension. References | Related Articles | Metrics

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GLOBAL EXISTENCE FOR QUASILINEAR  |WAVE EQUATION WITH A LOCALIZED WEAKLY NONLINEAR DISSIPATION IN EXTERIOR DOMAINS Jeong Ja Bae Acta mathematica scientia,Series B. 2009, 29 (5):  1203-1215.  DOI: 10.1016/S0252-9602(09)60097-7 Abstract ( 715 )   RICH HTML PDF (174KB) ( 1174 )   Save It is  proved that the global existence for the nonhomogeneous quasilinear wave equation with a localized weakly nonlinear dissipation in exterior domains. References | Related Articles | Metrics

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A NOTE ON LARGE TIME BEHAVIOUR OF SOLUTIONS FOR VISCOUS CAHN-HILLIARD EQUATION LIU Chang-Chun, ZHOU Juan, YIN Jing-Xue Acta mathematica scientia,Series B. 2009, 29 (5):  1216-1224.  DOI: 10.1016/S0252-9602(09)60098-9 Abstract ( 900 )   RICH HTML PDF (153KB) ( 1526 )   Save This article is devoted to the discussion of large time behaviour  of solutions for viscous Cahn-Hilliard equation with spatial dimension n ≤ 5. Some results on global existence of weak solutions for small initial value and  blow-up of solutions for any nontrivial initial value are established. References | Related Articles | Metrics

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DIRICHLET PROBLEMS FOR STATIONARY VON NEUMANN-LANDAU WAVE EQUATIONS CHEN Ze-Qan Acta mathematica scientia,Series B. 2009, 29 (5):  1225-1232.  DOI: 10.1016/S0252-9602(09)60099-0 Abstract ( 664 )   RICH HTML PDF (155KB) ( 1054 )   Save In this article, we are concerned with the Dirichlet problem of the stationary von Neumann--Landau wave equation: { ( -Δx + Δy ) Φ (x, y) = 0,     x, y ∈ Ω    Φ | ∂Ω×∂Ω = f, where Ω is a bounded domain in Rn. By introducing anti-inner product spaces, we show the existence and uniqueness of the generalized solution for the above Dirichlet problem by functional-analytic methods. References | Related Articles | Metrics

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BOUNDARY LAYER SOLUTION FOR  p-SYSTEM WITH ARTIFICIAL VISCOSITY QIN Xiao-Hong Acta mathematica scientia,Series B. 2009, 29 (5):  1233-1240.  DOI: 10.1016/S0252-9602(09)60100-4 Abstract ( 705 )   RICH HTML PDF (155KB) ( 1184 )   Save An initial-boundary values  problem in the half space (0, ∞) for p-system with artificial viscosity is investigated. It is shown that there exists a boundary layer solution. It is further proved that the boundary layer solution is nonlinear stable with arbitrarily  large perturbation. The proof is given by an elementary energy method. References | Related Articles | Metrics

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POINTWISE CONVERGENCE FOR EXPANSIONS IN SPHERICAL MONOGENICS FEI Ming-Gang, QIAN Tao Acta mathematica scientia,Series B. 2009, 29 (5):  1241-1250.  DOI: 10.1016/S0252-9602(09)60101-6 Abstract ( 847 )   RICH HTML PDF (180KB) ( 1181 )   Save We offer a new approach to deal with the pointwise convergence of Fourier-Laplace series on the unit sphere of even-dimensional Euclidean spaces. By using spherical monogenics defined through the generalized Cauchy-Riemann operator, we obtain the spherical monogenic expansions of square integrable functions on the unit sphere. Based on the generalization of Fueter's theorem inducing monogenic functions from holomorphic functions in the complex plane and the classical Carleson's theorem, a pointwise convergence theorem on the new expansion is proved. The result is a generalization of Carleson's theorem to the higher dimensional Euclidean spaces. The approach is simpler than those by using special functions, which may have the advantage to induce the singular integral approach for pointwise convergence problems on the spheres. References | Related Articles | Metrics

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MULTIRESOLUTION ANALYSIS, SELF-SIMILAR TILINGS AND HAAR WAVELETS ON THE HEISENBERG GROUP LIU He-Ping, LIU Yu, WANG Hai-Hui Acta mathematica scientia,Series B. 2009, 29 (5):  1251-1266.  DOI: 10.1016/S0252-9602(09)60102-8 Abstract ( 637 )   RICH HTML PDF (208KB) ( 1518 )   Save In this article, the properties of multiresolution analysis and  self-similar tilings on the Heisenberg group are studied. Moreover, we establish a theory to construct  an orthonormal Haar wavelet base in $L^2({\mathbb H}^d)$ by using self-similar tilings for the acceptable dilations on the Heisenberg group. References | Related Articles | Metrics

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SOLVING COLORED YANG-BAXTER EQUATION BY WU'S METHOD REN Xin-An, WANG Shi-Kun, WU Ke Acta mathematica scientia,Series B. 2009, 29 (5):  1267-1294.  DOI: 10.1016/S0252-9602(09)60103-X Abstract ( 719 )   RICH HTML PDF (248KB) ( 1273 )   Save In this article, we discuss nonsymmetric solutions of the colored Yang-Baxter equation dependent on spectral as well as colored parameters and give all seven-vertex solutions by Wu's method. It is also proved that the solutions are composed of six groups of basic solutions up to five solution transformations. Moreover, all solutions can be classified into two categories called Baxter type and free-fermion type. References | Related Articles | Metrics

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GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR FOR AN 1-D COMPRESSIBLE ENERGY TRANSPORT MODEL LI Yong Acta mathematica scientia,Series B. 2009, 29 (5):  1295-1308.  DOI: 10.1016/S0252-9602(09)60104-1 Abstract ( 628 )   RICH HTML PDF (180KB) ( 1266 )   Save In this article, the global existence and the large time behavior of smooth solutions to the initial boundary value problem for a degenerate compressible energy transport model are established. References | Related Articles | Metrics

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UNIQUENESS, ERGODICITY AND UNIDIMENSIONALITY OF INVARIANT MEASURES UNDER A MARKOV OPERATOR TANG Jun-Min, ZHANG Ji-Hong, ZHANG Xiong-Ying Acta mathematica scientia,Series B. 2009, 29 (5):  1309-1322.  DOI: 10.1016/S0252-9602(09)60105-3 Abstract ( 636 )   RICH HTML PDF (213KB) ( 1046 )   Save Let X be a compact metric space and C(X) be the space of all continuous functions on X. In this article, the authors consider the Markov operator T:C(X)N → C(X)N defined by Tf = (∑j=1Np1j fj ο w1j, …, ∑j=1N pNj fj ο wNj) for any f =(f 1, f 2, …, f N), where (p ij) is a N × N transition probability matrix and {w ij} is an family of continuous transformations on X. The authors study the uniqueness, ergodicity and unidimensionality of T*-invariant measures where T* is the adjoint operator of T. References | Related Articles | Metrics

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MULTIPLE SOLUTIONS FOR THE SCHRÖDINGER EQUATION WITH MAGNETIC FIELD PENG Chao-Quan, YANG Jian-Fu Acta mathematica scientia,Series B. 2009, 29 (5):  1323-1340.  DOI: 10.1016/S0252-9602(09)60106-5 Abstract ( 748 )   RICH HTML PDF (222KB) ( 1041 )   Save The authors consider the semilinear Schrödinger equation -ΔAu+ Vλ(x)u=Q(x)|u|γ-2 u  in  RN, where 1< γ < 2* and γ≠ 2, Vλ = V+ - λV-. Exploiting the relation between the Nehari manifold and fibrering maps,  the existence of nontrivial solutions for the problem is discussed. References | Related Articles | Metrics

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A NOTE ON CONVOLUTION-TYPE CALDERÓN-ZYGMUND OPERATORS YANG Zhan-YIng, YANG Qi-Xiang Acta mathematica scientia,Series B. 2009, 29 (5):  1341-1350.  DOI: 10.1016/S0252-9602(09)60107-7 Abstract ( 829 )   RICH HTML PDF (189KB) ( 1347 )   Save For convolution-type Calderón-Zygmund operators, by the boundedness on Besov spaces and Hardy spaces, applying interpolation theory and duality, it is  known that Hörmander condition can ensure the boundedness on Triebel-Lizorkin spaces Fp0,q(1< p, q < ∞)  and on a party of endpoint spaces F10,q(1 ≤ q ≤ 2), but this idea is invalid for endpoint Triebel-Lizorkin spaces F10,q(2 < q ∞). In this article, the authors apply wavelets and interpolation theory to establish the boundedness on F10,q(2 < q ≤ ∞) under an integrable condition which approaches Hörmander condition infinitely. References | Related Articles | Metrics

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CONVERGENCE RATES FOR THE COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH GENERAL FORCE QIAN Jian-Zhen, YIN Hui Acta mathematica scientia,Series B. 2009, 29 (5):  1351-1365.  DOI: 10.1016/S0252-9602(09)60108-9 Abstract ( 966 )   RICH HTML PDF (212KB) ( 1250 )   Save For the viscous and heat-conductive fluids governed by the compressible Navier-Stokes equations with external force of general form in R3, there exist nontrivial stationary solutions provided the external forces are small in suitable norms, which was studied in article [15], and there we also proved the global in time stability of the stationary solutions with respect to initial data in H3-framework. In this article, the authors investigate the rates of convergence of nonstationary solutions to the corresponding stationary solutions when the initial data are small in H3 and bounded in L6/5. References | Related Articles | Metrics

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GENERALIZATIONS AND CARTESIAN CLOSED SUBCATEGORIES OF SEMICONTINUOUS LATTICES LI Qiang-Guo, WU Xiu-Hua Acta mathematica scientia,Series B. 2009, 29 (5):  1366-1374.  DOI: 10.1016/S0252-9602(09)60109-0 Abstract ( 707 )   RICH HTML PDF (160KB) ( 1248 )   Save In this article, the authors mainly study how to obtain new semicontinuous lattices from the given semicontinuous lattices and discuss the conditions under which the image of a semicontinuous projection operator is also semicontinuous. Moreover, the authors investigate the relation between semicontinuous lattices and completely distributive lattices. Finally, it is proved that the strongly semicontinuous lattice category is a Cartesian closed category. References | Related Articles | Metrics

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THE APPLICATION OF THE KINETIC FORMULATION TO A SYSTEM OF QUADRATIC FLUX CHENG Zhi-Xin Acta mathematica scientia,Series B. 2009, 29 (5):  1375-1382.  DOI: 10.1016/S0252-9602(09)60110-7 Abstract ( 751 )   RICH HTML PDF (150KB) ( 959 )   Save In this article, the author uses the compensated compactness method coupled with some basic ideas of the kinetic formulation developed by Lions, Perthame, Souganidis and Tadmor to give a refined proof for the existence of global entropy solutions to a system of quadratic flux. The fire-new method of reduction of Young measures is a pith of this work. References | Related Articles | Metrics

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LYAPOUNOV EXPONENTS AND LAW OF LARGE NUMBERS FOR RANDOM WALK IN RANDOM ENVIRONMENT WITH HOLDING TIMES MAO Ming-Zhi, HAN Dong Acta mathematica scientia,Series B. 2009, 29 (5):  1383-1394.  DOI: 10.1016/S0252-9602(09)60111-9 Abstract ( 686 )   RICH HTML PDF (203KB) ( 1046 )   Save In this article, the authors mainly discuss the law of large number under Kalikow's condition for multi-dimensional random walks in random environment with holding times. The authors give an expression to the escape speed of random walks in terms of the Lyapounov exponents, which have been precisely used in the context of large deviation. References | Related Articles | Metrics

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SOME NEW FAMILIES OF FILTRATION FIVE IN THE STABLE HOMOTOPY OF SPHERES LIN Jin-Kun Acta mathematica scientia,Series B. 2009, 29 (5):  1395-1404.  DOI: 10.1016/S0252-9602(09)60112-0 Abstract ( 692 )   RICH HTML PDF (185KB) ( 900 )   Save This study proves a general result on convergence of  α2 x ∈ ExtAs+2, tq+2q+1(Zp, Zp) in the Adams spectral sequence and as a consequence, the study detects some new families in the stable homotopy groups of spheres πtq+2q-4S which is represented in the Adams spectral sequence by α2fn, α2f'n, ，α2huhmhn ∈ ExtA5, tq+2q+1(Zp, Zp) with tq = pn+1q+2pnq, 2pn+1q+pnq, puq+pmq+pnq, respectively, where α2 ∈Exta2, 2q+1Zp, Zp), fn ∈ ExtA3, pn+1q+2pnq(Zp, Zp), f'n ∈ ExtA3, 2pn+1q+pnq (Zp, Zp), hn ∈ ExtA1,pnq(Zp, Zp) and p ≥ 5 is a prime, q = 2(p-1), n ≥ 2. References | Related Articles | Metrics

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NONTRIVIAL SOLUTIONS FOR  SCHRÖDINGER EQUATIONS LIU Fang, YANG Jian-Fu Acta mathematica scientia,Series B. 2009, 29 (5):  1405-1420.  DOI: 10.1016/S0252-9602(09)60113-2 Abstract ( 869 )   RICH HTML PDF (218KB) ( 1074 )   Save The authors prove the existence of nontrivial solutions for the Schrödinger equation -Δu + V(x) u = λ f(x, u) in RN, where f is superlinear, subcritical and critical at infinity, respectively, V is periodic. References | Related Articles | Metrics

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COBORDISM CLASSES OF FIBERINGS OVER PRODUCT OF PROJECTIVE SPACES WANG Yan-Ying, LI Jing-Yan Acta mathematica scientia,Series B. 2009, 29 (5):  1421-1429.  DOI: 10.1016/S0252-9602(09)60114-4 Abstract ( 696 )   RICH HTML PDF (159KB) ( 943 )   Save Let RP(k) denote the k-dimensional real projective space. This article determines which cobordism classes are represented by the total space of a fibering with prescribed base space RP(3)\times RP(1), RP(2)×RP(1), RP(2)\times RP(1)×RP(1) or $RP(3)\times RP(2). References | Related Articles | Metrics

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COMPOSITION TYPE OPERATORS FROM HARDY SPACES TO μ-BLOCH SPACES ON THE UNIT BALL WANG Xiong-Liang, LIU Ta-Shun Acta mathematica scientia,Series B. 2009, 29 (5):  1430-1438.  DOI: 10.1016/S0252-9602(09)60115-6 Abstract ( 849 )   RICH HTML PDF (181KB) ( 1287 )   Save Let φ be a holomorphic self-map of Bn and Ψ ∈ H(Bn). A composition type operator is defined by TΨ, φ(f)= Ψf ο φ  for f ∈ H(Bn), which is a generalization of  the multiplication operator and  the composition operator. In this article, the necessary and sufficient conditions are given for the composition type operator TΨ, φ  to be bounded or compact from  Hardy space Hp(Bn) to μ-Bloch space B(Bn). The conditions are some supremums concerned with Ψ, φ, their derivatives and Bergman metric of $\Bn$. At the same time, two corollaries are obtained. References | Related Articles | Metrics

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ATOMIC DECOMPOSITIONS AND |DUALS OF WEAK HARDY SPACES OF B-VALUED MARTINGALES MA Tao, LIU Pei-De Acta mathematica scientia,Series B. 2009, 29 (5):  1439-1452.  DOI: 10.1016/S0252-9602(09)60116-8 Abstract ( 825 )   RICH HTML PDF (200KB) ( 1307 )   Save In this article, several weak Hardy spaces of Banach-space-valued martingales are introduced, some atomic decomposition theorems for them are established and their duals are investigated. The results closely depend on the geometrical properties of the Banach space in which the martingales take values. References | Related Articles | Metrics

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ON A NEW SINGULAR DIRECTION OF QUASIMEROMORPHIC MAPPINGS WU Zhao-Jun, SUN Dao-Chun Acta mathematica scientia,Series B. 2009, 29 (5):  1453-1460.  DOI: 10.1016/S0252-9602(09)60117-X Abstract ( 831 )   RICH HTML PDF (157KB) ( 946 )   Save By applying Ahlfors' theory of covering surface, we establish a fundamental inequality for quasimeromorphic mapping in an angular domain. As an application, we prove the existence of a new singular direction for quasimeromorphic mapping f, namely, a precise S direction, for which the spherical characteristic function S(r, f) is used as a comparison function. References | Related Articles | Metrics

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CONVEX CONCENTRATION INEQUALITIES FOR CONTINUOUS GAS AND STOCHASTIC DOMINATION MA Yu Tao Acta mathematica scientia,Series B. 2009, 29 (5):  1461-1468.  DOI: 10.1016/S0252-9602(09)60118-1 Abstract ( 641 )   RICH HTML PDF (168KB) ( 905 )   Save In this article,  we consider the continuous gas in a bounded domain ∧of R+ or Rd described by a Gibbsian probability measure μη∧ associated with a pair interaction Φ, the inverse temperature β, the activity z>0, and the boundary condition η. Define F=∫f(s)ω∧(ds). Applying the generalized Ito's formula for forward-backward martingales (see Klein et al. [5]), we obtain convex concentration inequalities for F with respect to the Gibbs measure μη∧. On the other hand, by FKG inequality on the Poisson space, we also give a new simple argument for the stochastic domination for the Gibbs measure. References | Related Articles | Metrics

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REGULARITY OF THE SOLUTIONS FOR NONLINEAR BIHARMONIC EQUATIONS IN |RN DENG Yin-Bin, LI Yi Acta mathematica scientia,Series B. 2009, 29 (5):  1469-1480.  DOI: 10.1016/S0252-9602(09)60119-3 Abstract ( 766 )   RICH HTML PDF (188KB) ( 918 )   Save The purpose of this article is to establish the regularity of  the weak solutions for the nonlinear biharmonic equation {Δ2u+a(x)u=g(x, u),  u∈ H2 (RN),                     （1.1） where the condition u ∈ H2(RN) plays the role of a boundary value condition, and as well expresses explicitly that the differential equation is to be satisfied in the weak sense. References | Related Articles | Metrics

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RIEMANN BOUNDARY VALUE PROBLEM WITH RESPECT TO THE PERTURBATION  OF BOUNDARY CURVE TO BE AN OPEN ARC LIN Juan, WANG Chuan-Rong Acta mathematica scientia,Series B. 2009, 29 (5):  1481-1488.  DOI: 10.1016/S0252-9602(09)60120-X Abstract ( 812 )   RICH HTML PDF (158KB) ( 1270 )   Save By dint of the stability of Cauchy-type integral with kernel density of class H* for an open arc, this paper discusses the stability of the solution of Riemann boundary value problem with respect to the perturbation of boundary curve to be an open arc. References | Related Articles | Metrics

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EIGENVALUE PROBLEM OF ELLIPTIC EQUATIONS WITH HARDY POTENTIAL XIE Chao-Dong, CHEN Yao-Tian, YAO Yang-Xin Acta mathematica scientia,Series B. 2009, 29 (5):  1489-1496.  DOI: 10.1016/S0252-9602(09)60121-1 Abstract ( 646 )   RICH HTML PDF (158KB) ( 1201 )   Save Consider the eigenvalue problem of elliptic equations with Hardy potential. Improve the results of references by introducing a new Hilbert space and using integral inequality. References | Related Articles | Metrics