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25 April 2014, Volume 34 Issue 2 Previous Issue    Next Issue

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Solutions to Inhomogeneous Quasilinear Elliptic Problems with Concave-Convex Type Nonlinearities LIANG Zhan-Ping, SU Jia-Bao Acta mathematica scientia,Series A. 2014, 34 (2):  217-226.  Abstract ( 500 )   RICH HTML PDF (325KB) ( 404 )   Save In this paper we show that the inhomogeneous quasilinear elliptic equations {-div(Φ(|∨u|)∨u)=μ|u|q-2u+λ|u|p-2u in Ω,  u=0                                                        on∂Ω, where Ω ( RN is a bounded domain with smooth boundary ∂Ω, and μ, λ ∈ R are two parameters, possess infinitely many weak solutions in Orlicz-Sobolev space by using variational methods. References | Related Articles | Metrics

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The Existence of |Solution for p-Laplace Equation Involving Resonant Term ZENG Xiao-Yu, WAN Jun-Xia Acta mathematica scientia,Series A. 2014, 34 (2):  227-233.  Abstract ( 469 )   RICH HTML PDF (286KB) ( 365 )   Save In this paper, a class of p-Laplace equations involving  a term of asymptotically |u|p-2u at infinity  are studied under the Dirichlet boundary condition. By applying the  linking theorem, the existence of nontrivial solution is obtained  when  λ1≤λ<λ2 , where λ1 is the first eigenvalue of (-?p, W1, p0(Ω) ). References | Related Articles | Metrics

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The Effect of Delay on a Diffusive Predator-Prey System with Ivlev-Type Functional Response WANG Xue-Chen, WEI Jun-Jie Acta mathematica scientia,Series A. 2014, 34 (2):  234-250.  Abstract ( 504 )   RICH HTML PDF (731KB) ( 629 )   Save A delayed diffusive predator-prey system with Ivlev-type predator functional response subject to Neumann boundary conditions is considered. The stability of nonnegative equilibria and existence of Hopf bifurcation are obtained by analyzing the distribution of the eigenvalues. By the theory of normal form and center manifold, an explicit algorithm for determining the stability and direction of periodic solution bifurcating from Hopf bifurcation is derived. References | Related Articles | Metrics

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Gauge Transformation Between the Isospectral and First-Order Nonisospectral Kaup-Newell Hierarchies XUE Yu-Shan Acta mathematica scientia,Series A. 2014, 34 (2):  251-258.  Abstract ( 411 )   RICH HTML PDF (272KB) ( 419 )   Save In this paper, the gauge transformation between the isospectral and first-order nonisospectral Kaup-Newell (KN) spectral problems is derived by introducing the isospectral and first-order nonisospectral Ablowitz-Kaup-Newell-Segur system. Besides, the equivalence relation between the isospectral and first-order nonisospectral KN hierarchies is given. References | Related Articles | Metrics

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The Weakly Damped Nonlinear Hartree Equation HUANG Juan, ZHANG Jian Acta mathematica scientia,Series A. 2014, 34 (2):  259-265.  Abstract ( 391 )   RICH HTML PDF (307KB) ( 313 )   Save This paper is concerned with the weakly damped nonlinear Hartree equation which has many interesting applications in quantum theory. We discuss the global existence of this equation from two aspects, the damped coefficients and the initial data, respectively. By Strichartz estimate, we obtain a global existence result which depends on the size of the damped parameter. We also get the other global existence result depending on the initial data. Moreover, a small initial data criterion of global existence is obtained. References | Related Articles | Metrics

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Stability of Cubic Functional Equations in Banach Spaces CHENG Li-Hua, LIAN Tie-Yan Acta mathematica scientia,Series A. 2014, 34 (2):  266-273.  Abstract ( 535 )   RICH HTML PDF (270KB) ( 465 )   Save In this note, we will find out the general solution and investigate the Hyers-Ulam-Rassias stability of a cubic functional equation af(x+ay)-f(ax+y)=a(a2-1)/2[f(x+y)+f(x-y)]+(a4-1)f(y)-2a(a2-1)f(x), in Banach spaces for a fixed integer a with a≠0, ±1. Forthermore, we give the equivalent proof of eight functional equations. At last, the stability of cubic functional equation in Banach spaces is dissucied. References | Related Articles | Metrics

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Non-Triviality of the Product b0k0δs+4 in the Adams Spectral Sequence ZHONG Li-Nan, LIU Xiu-Gui Acta mathematica scientia,Series A. 2014, 34 (2):  274-282.  Abstract ( 485 )   RICH HTML PDF (284KB) ( 317 )   Save In this paper, we make use of the modified May spectral sequence to prove the nontriviality of the product b0k0δs+4∈ExtAs+8, t(Zp, Zp), where p≥7 is a prime, 0≤s <p-4, q=2(p-1), and t =(s+4)p3q+(s+3)p2q+(s+5)pq+(s+2)q+s. References | Related Articles | Metrics

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Hybrid Shrinking Projection Method for a Countable Family of Total Quasi-Φ-Asymptotically Nonexpansive Mappings, a Generalized Mixed Equilibrium Problem and a Maximal Monotone Operator ZHU Jin-Hua Acta mathematica scientia,Series A. 2014, 34 (2):  283-302.  Abstract ( 399 )   RICH HTML PDF (406KB) ( 329 )   Save The purpose of this paper is first to introduce the concept of total quasi-Φ-asympto- tically nonexpansive mapping and then consider a hybrid shrinking projection method for finding a common element of the set GMEP of solutions of a generalized  mixed equilibrium problem, the set ∩∞i=1F(Si) of common fixed points of a countable family of total quasi-Φ-asymptotically nonexpansive mappings {Si}∞i=1 and the set T-10 of zeros of a maximal monotone operator T in a uniformly smooth and strictly convex Banach space with Kadec-Klee property. It is proven that under appropriate conditions, the sequence generated by the hybrid shrinking projection method, converges strongly to some point in GMEP ∩T-10 ∩(∩∞i=1F(Si)). This new result represents the improvement, complement and development of the previously known ones in the literature. References | Related Articles | Metrics

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Weighted Estimates for Commutators of Marcinkiewicz Integrals with Non-Doubling Measures LU Sheng-Dong, JIANG Yin-Sheng, WANG Song-Bai Acta mathematica scientia,Series A. 2014, 34 (2):  303-316.  Abstract ( 428 )   RICH HTML PDF (364KB) ( 323 )   Save Let μ be a nonnegative Radon measure on Rd which only satisfies μ(B(x, r))≤C0 rn, for all x ∈Rd , r>0, n∈(0, d] and some fixed constants C0 >0. In this paper, a weak type estimate with App(μ) weight is established for commutators generated by Marcinkiewicz integrals operators with RBMO functions. References | Related Articles | Metrics

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Zeros of Differential Polynomials and Normal Criterions LU Qian, LIAO Qi-Long Acta mathematica scientia,Series A. 2014, 34 (2):  317-326.  Abstract ( 429 )   RICH HTML PDF (325KB) ( 362 )   Save Let F be a family of meromorphic function in a plane domain D, all of whose poles is of multiplicity k at least and zeros are of multiplicity s at least. Suppose that a and b are two complex numbers, a, b∈C, a≠0. If for every pair function f(z), g(z)∈F, f(k)-af3 and g(k)-ag3 share a value b, then F is normal in D, where s=3 as k=2, s=k as k≥3. References | Related Articles | Metrics

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Crossed Products of Weak Hopf Group Coalgebras GUO Shuang-Jian, WANG Shuan-Hong Acta mathematica scientia,Series A. 2014, 34 (2):  327-337.  Abstract ( 420 )   RICH HTML PDF (314KB) ( 312 )   Save In this paper, the authors introduce the notion of a weak group crossed product and give a sufficient and necessary condition under which weak group crossed product algebras and the usual tensor product coalgebra become a weak semi-Hopf group-coalgebra. Finally, we prove a duality theorem for weak group  crossed products, which extends the main results given by Shen and Wang[7, 8]. References | Related Articles | Metrics

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Blow-up and Global Existence of Solutions to a Degenerate Parabolic System with Nonlocal Boundaries LING Zheng-Qiu, ZHOU Ze-Wen Acta mathematica scientia,Series A. 2014, 34 (2):  338-346.  Abstract ( 464 )   RICH HTML PDF (321KB) ( 313 )   Save This paper deals with a degenerate parabolic system with nonlinear nonlocal sources and nonlocal boundary conditions. With the help of the super- and sub-solution methods, the blow-up and global existence conditions of positive solutions are obtained. These results not only extend those in [8], but also show that the global existence and blow-up results depend on the weight functions g1(x, y), g2(x, y) and the size of a, b, l1, l2. References | Related Articles | Metrics

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Boundedness of Multilinear Commutators Generated by Singular Integral Operators with Non-Smooth Kernel on Spaces of Homogeneous Type SUN Ai-Wen, WANG Yong-Yan, SHU Li-Sheng Acta mathematica scientia,Series A. 2014, 34 (2):  347-357.  Abstract ( 444 )   RICH HTML PDF (309KB) ( 322 )   Save In this paper, we main discuss the boundedness of multilinear commutators generated by singular integral operators with non-smooth kernel T and b(b\in {\rm Lip}_{\beta}) from Lp(X) to Fp, Amβ, ∞(X). References | Related Articles | Metrics

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Some New Coupled Fixed Point Theorems in Partially Ordered G-Metric Spaces GU Feng, XIE Hong-Qing Acta mathematica scientia,Series A. 2014, 34 (2):  358-366.  Abstract ( 350 )   RICH HTML PDF (298KB) ( 472 )   Save In this paper, we introduce a new contractive condition into the G-metric spaces, and several new coupled coincidence point theorems are established in G-metric spaces. The obtained results in this article extend and improve the recent relative results. References | Related Articles | Metrics

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Semi-Strong Solutions to Hydrodynamic Flow of Liquid Crystals GAO Zhen-Sheng, JIANG Fei, WANG Wei-Wei Acta mathematica scientia,Series A. 2014, 34 (2):  367-377.  Abstract ( 394 )   RICH HTML PDF (371KB) ( 295 )   Save In this paper, we show the existence of semi-strong solutions to hydrodynamic flow of the two-dimensional nematic liquid crystals with small initial data, even though the initial density does not  possess the positive lower bound  in  Ω. The main novelty of the paper lies in the fact that our new estimate of ||∂, d|L4/3(I, L2Ω)) is independent of the lower-bound of ρ, where d and ρ represent the director of the molecules and the density of the fluid, respectively. References | Related Articles | Metrics

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Non-Monotone Smoothing Newton Algorithm for SCLP Based on a Scaled Central Path NI Tie, LIU Xiao-Hong Acta mathematica scientia,Series A. 2014, 34 (2):  378-392.  Abstract ( 463 )   RICH HTML PDF (425KB) ( 280 )   Save Based on a modified version of the Chen-Harker-Kanzow-Smale (CHKS) smoothing function, this paper investigates a non-monotone smoothing Newton algorithm with a scaled central path for solving linear programming over symmetric cones (SCLP). By using the theory of Euclidean Jordan algebras, we show that the proposed algorithm is globally and locally superlinearly convergent under suitable assumptions. Some preliminary numerical results is shown that our algorithm proposed is promising. References | Related Articles | Metrics

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Oscillation Criteria for Second-Order Dynamic Equations with Positive and Negative Coefficients and Damping on Time Scales YANG Jia-Shan Acta mathematica scientia,Series A. 2014, 34 (2):  393-408.  Abstract ( 592 )   RICH HTML PDF (420KB) ( 376 )   Save The oscillation for certain second-order nonlinear variable delay dynamic equations with positive and negative coefficients and damping and nonlinear neutral on time scales is discussed. By using the time scales theory and the generalized Riccati transformation and the inequality technique, we establish some new oscillation criteria for the inequations. Our results extend and improve some known results, but also unify the oscillation of second-order nonlinear delay differential equations with damping and second-order nonlinear delay difference equations with damping. References | Related Articles | Metrics

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The Interior Transmission Problem for Isotropic Maxwell Equations and Some Estimates on the Index of Refraction QU Feng-Long, WANG Yu-Quan Acta mathematica scientia,Series A. 2014, 34 (2):  409-418.  Abstract ( 483 )   RICH HTML PDF (337KB) ( 353 )   Save This paper is concerned with the global existence of uniformly bounded solutions for a class of chemotaxis models in two dimensional spaces. By using detailed energy estimates, some a priori estimates in different types of spaces including V2(Qt, t+1)、W1, 2p, p(Qt, t+1)、Lp, q(Qt, t+1)) and by applying uniform Gronwall inequality, we  can prove  the global existence of uniformly bounded solutions for a class of chemotactic systems with the proliferation term which involves both growth and death of the bacteria. References | Related Articles | Metrics

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A Global Topological Structure of a Class of Cubic Quasi-Homogeneous Vector Fields HUANG Gai-Gai, FENG Guang-Ting, ZHANG Xing-An Acta mathematica scientia,Series A. 2014, 34 (2):  419-425.  Abstract ( 451 )   RICH HTML PDF (358KB) ( 336 )   Save In this paper,we use the idea of the central projection transformation to prove that the geometric properties of a class of cubic vector field depends on its tangent vector and induced vector field. We investigate its topological structures and classified, and we obtain 25 types of different topological classification of this vector field. References | Related Articles | Metrics

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CBMO Estimates for Higher-Order Commutators onHomogeneous Morrey-Herz Spaces WANG Li-Wei, QU Meng, SHU Li-Sheng Acta mathematica scientia,Series A. 2014, 34 (2):  426-436.  Abstract ( 402 )   RICH HTML PDF (313KB) ( 346 )   Save In this paper, we establish CBMO estimates for the higher-order commutators of Hardy-Littlewood maximal operator and fractional maximal operator with rough kernels. Also, the corresponding results for the higher-order commutators which are generated by a class of sublinear operators are obtained. References | Related Articles | Metrics

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Asymptotic Behavior of Solutions for Second-Order Semilinear Singularly Perturbed Boundary Value Problem LIU Shuai, ZHOU Zhe-Yan, SHEN Jian-He Acta mathematica scientia,Series A. 2014, 34 (2):  437-444.  Abstract ( 384 )   RICH HTML PDF (345KB) ( 368 )   Save In this paper, the asymptotic behavior of solutions for second-order semi-linear singularly perturbed boundary value problems without normal hyperbolicity is studied. By using the method of boundary layer function, we construct the algebraic boundary layers and hence obtain the uniformly valid asymptotic solution and give the error estimate between the asymptotic and exact solutions via the way of differential inequalities. The correctness of the theoretical result is verified through a typical examples. References | Related Articles | Metrics

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Regularity and Global Attractor of Nonlinear Elastic Rod Oscillation Equation MA Wen-Jun, MA Qiao-Zhen, GAO Pei-Ming Acta mathematica scientia,Series A. 2014, 34 (2):  445-453.  Abstract ( 438 )   RICH HTML PDF (307KB) ( 325 )   Save In this paper, we establish the regularity of nonlinear elastic rod oscillation equation. Furthermore, the existence of (H10(Ω)×H10(Ω), (H2(Ω)∩H10(Ω))×(H2(Ω)∩H10(Ω))) global attractor is proved. References | Related Articles | Metrics

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The Growth of a Class of Analytic Zero Order and Finite Order Laplace-Stieltjes Transform on the Plane YANG Qi, CAO Yue-Bo, TIAN Hong-Gen Acta mathematica scientia,Series A. 2014, 34 (2):  454-462.  Abstract ( 416 )   RICH HTML PDF (307KB) ( 416 )   Save By using a Type-function, the growth a class of analytic zero order and finite order Laplace-Stieltjes transform on the plane is investigated. And three theorems are obtained. References | Related Articles | Metrics

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Characterization of Centralizers and Generalized Derivations on J-Subspace Lattice Algebras QI Xiao-Fei Acta mathematica scientia,Series A. 2014, 34 (2):  463-472.  Abstract ( 445 )   RICH HTML PDF (341KB) ( 442 )   Save Let L be a J-subspace lattice on a Banach space X and AlgL the associated J-subspace lattice algebra. Assume that Φ: AlgL→AlgL is an additive map and dimK≥2 for every K∈J(L).  It is shown that the following statements are equivalent: (1) Φ is a centralizer; (2) Φ sataisies Φ(A)B=AΦ(B)=0 whenever A, B∈AlgL with AB=0; (3) Φ satisfies Φ(A)B+Φ(B)A=AΦ(B)+B\Φ(A)=0 whenever A, B∈AlgL with  AB+BA=0; (4) Φ satisfies Φ(A)BC+Φ(C)BA=ABΦ(C)+CBΦ(A)=0 whenever A, B∈AlgL with ABC+CBA=0. As an application, additive maps generalized derivable at zero on AlgL are characterized. References | Related Articles | Metrics