In this paper, we study the decomposition of Nehari manifold for the Brézis-Nirenberg problem with nonhomogeneous Dirichlet boundary conditions. By using this result, the Lusternik-Schnirelman category and the minimax principle, we establish a multiple result(four solutions) for the Brézis-Nirenberg problem with nonhomogeneous Dirichlet boundary conditions.
In this paper, we study the existence of the traveling wave solutions for some Keller-Segel systems. For both parabolic-parabolic, and parabolic-differential types, we show the existence of the positive traveling wave solutions and investigate their speeds.
The purpose of this paper is to give some sufficient conditions for the existence and uniqueness of solutions to the fractional differential equation as follows Dαx(t)=f(t,x(t)),t∈J:=(0,1], 0<α<1, t1-αx(t)=x(1), where Dα denotes the Riemann-Liouville fractional derivative, f may be singular at t=0. Lower and upper solutions method, maximum principle together with iterative technique are employed. An example is presented to illustrate the application of results obtained.
Consider the time-harmonic electromagnetic plane waves incident on a chiral curved layer covering a perfectly conducting object. A two-dimensional scattering model is established and the existence and the uniqueness of solutions are studied by an integral equation method. We have shown that the integral equation system admits a unique solution.
In this article, we introduce the concepts of QCLkR spaces and QCLkS spaces and show that QCLkR spaces and QCLkS spaces are dual concepts by using the local reflexive principle. Also, we give some characteristic descriptions of QCLkR spaces and QCLkS spaces by using the slice of unit ball, and discuss the relation between QCLkR spaces, QCLkS spaces with other convexity and smoothness. The results perfect the research on convexity and smoothness about Banach spaces.
In this paper, we obtain a quasinormal criterion of meromorphic functions and give an example of application in the value distribution theory.
Let ω∈A1, 0<α<mn and 0<β<1 such that α+β<mn, and let 1<p1,…,pm<∞ with 1/q=1/p-(α+β)/n>0 and 1/p=1/p1+…+1/pm. We obtain that b∈Lipβ(ω)m if and only if the commutators[Σb,Iα] generated by multilinear fractional integral operators Iα and the symbols b are bounded from Lp1(ω)× …× Lpm(ω) to Lq(ω1-(1-α/n)q).
The purpose of this paper is to study the constrained split common fixed point problem. We suggest and analyze three kinds of iterative algorithms for solving the problem. Several strong convergence theorems have been established, which improve and extend the related results obtained by some authors.
In this paper, we study random iterative convergence problem on bounded strictly convex and bounded weak convex domain in Cn based on the classical Wolff-Denjoy theorem. On bounded strictly convex domain, we prove that there exists a supsequence which converges uniformly to constant map on the boundary under some condition. On bounded weak convex domain, the restrictive condition becomes stronger, but the convergence result becomes weaker. The method in this paper can be used to prove the iterative theorem of single analytic function.
In this paper, a modified proximal gradient method is proposed for solving a class of nonsmooth convex optimization problems, which arises in many contemporary statistical and signal applications. The proposed method adopts the self-adaptive stepsize. In addition, it is linearly convergent without the assumption of the strong convexity of the objective function.
This paper proves an upper bound of fractal dimension of the kernel sections for the long-wave-short-wave resonance equations on infinite lattices.
In this paper, we prove some uniqueness theorems for meromorphic mappings from Cm into Pn(C) with few moving targets, which improve and extend some earlier work.
In this note, we study the viability of a bounded open domain in Rn for a process driven by a path-dependent stochastic differential equation with Lipschitz data. We extend an invariant result of Cannarsa, Prato and Frankowska to a non-Markovian setting.
We consider the symmetric random walk with stay in this paper, whose local time can be represented by a function of a non-primitive two-type branching process. Using this representation, we establish the convergence of the local time of the random walk.
In this paper, the generalized non-linear Markov branching model with resurrection is considered. Some properties of the generating functions for generalized non-linear Markov branching q-matrix with resurrection are firstly investigated. By using the generating functions of the corresponding q-matrix, the criteria for regularity and uniqueness for such structure are firstly established, and the explicit expressions for the extinction probabilities and mean extinction times are presented. The stability properties and ergodicity of the model with resurrection are then investigated. The conditions for recurrence, ergodicity are obtained. An explicit expression for the equilibrium distribution is further presented.
When the Difference Theorem is applied to calculating the derivative of discrete data, the measure-error can lead to inaccurate result or some of the data having no result. To resolve these problems, the necessary and sufficient conditions for identifying approximative inflexions of the difference-curve are obtained by analyzing and deducing applying conditions of the Difference Theorem on condition that the data are at equal intervals. In the condition of measure-error existing, the applying conditions of the Difference Theorem are obtained by analyzing, and test and verified by using test-function. The results are compared with those from center-smoothing algorithm, cubic spline algorithm and different fitting models. The factors which can affect application effects of the Difference Theorem are analyzed and validated by using measurement data. The detailed method of calculating second order derivative with the Difference Theorem and it's deduction is put forward.
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