共振情形下二阶多点边值问题解的存在性

运用Mawhin重合度理论,讨论了共振情形下一类二阶多点边值问题解的存在性,在算子L满足Ker L=2的条件下,获得了该问题解的存在性结果.     

指数二分性与退化情形下的异宿分支

利用指数型二分性理论,研究了较高退化程度下的异宿分支理论;给出了一个能确定系统在退化情形下横截同、异宿轨道存在性的Melnikov向量;提供了一个处理高维退化情形下横截同、异宿轨道存在性的泛函分析方法.     

二阶p-Laplace多参数离散周期边值问题三个解的存在性

研究了二阶p-Laplace含多个参数的非线性离散周期边值问题,获得了非线性项在更一般的情形下三个解的存在性定理.主要结论的证明基于临界点理论.     

一类非局部反应扩散方程组Cauchy问题的临界爆破指标

证明了一类来源于燃烧理论的非局部反应扩散方程组Cauchy问题解的局部存在性、唯一性及临界爆破指标的存在性。并证明临界爆破指标属于爆破情形。     

离散广义Emden-Fowler方程的边值问题

应用临界点理论, 得到离散广义Emden-Fowler方程边值问题解的存在性的若干充分条件．对一类特殊情形, 其解的存在性条件是最佳的．对线性情形, 应用离散变分理论, 给出了上述方程边值问题解的存在性、唯一性以及多重性的充分必要条件.     

关于一类新型的具边值条件的曲率流问题

本文提出了一类带有边界条件的新的曲率流问题,说明了它们的理论来源和实际背景.对Gauss曲率情形,建立了这种曲率流古典解的存在唯一性,并用一种适用于更一般曲率情形的方法,研究了这种曲率流的渐近性。     

非平稳NA序列部分和的精确渐近性

本文探讨了非平稳NA序列部分和的精确渐近性．以前的文献在讨论NA序列此类极限性质时都附加有强平稳条件的限制,这必然会给一些问题的研究带来不便．周知,非平稳NA序列在许多实际问题中是大量存在的,所以解除强平稳条件的束缚具有较大的理论和实际意义,这正是本文的目的之所在,同时本文也将已有的一些结果包含成为特殊情形．     

一类临界拟线性椭圆型方程组解的存在性

本文讨论了一类临界拟线性椭圆型方程组解的存在性问题.利用LionsPL提出的第二集中紧性原理和山路引理,证明了该方程组在超线性扰动情形下非平凡解的存在性.此外,利用极值原理,也得到了该方程组在次线性扰动情形存在非平凡解.     

关于一类新型的具边值条件的曲率流问题

本文提出了一类带有边界条件的新的曲率流问题,说明了它们的理论来源和实际背景对Ｇａｕｓｓ曲 率情形,建立了这种曲率流古典解的存在唯一性,并用一种适用于更一般曲率情形的方法,研究了这 种曲率流的渐近性。     

带临界指数传输问题解的存在性研究

本文通过变分方法推广一类带权函数和临界指数的传输问题,先利用对称山路引理获得次临界情形无穷多解的存在性,再利用山路引理得到临界情形有限个正解的存在性.     

p-Laplace方程Neumann边值问题的可解性

主要讨论了一维p-Laplace方程(φp(u′))′=f(t,u,u′),t∈(0,1))在Neumann边值条件u′(0)=0,u′(1)=0下边值问题解的存在性,其中φp(s)=|s|p-2s,s≠0.文中通过使用Leray-Schauder度原理,在适当的条件下,建立了对于p-Laplace方程在共振情形下Neumann边值问题解的存在性的充分条件.     

一类二阶离散Neumann边值问题正解的存在性

研究一类二阶离散Neumann边值问题正解的存在性,运用不动点指数理论获得了方程存在正解的最优条件,并给出一个具体例子说明这一结果。     

Boundary pairs associated with quadratic forms

We introduce a purely functional analytic framework for elliptic boundary value problems in a variational form. We define abstract Neumann and Dirichlet boundary conditions and a corresponding Dirichlet‐to‐Neumann operator, and develop a theory relating resolvents and spectra of these operators. We illustrate the theory by many examples including Jacobi operators, Laplacians on spaces with (non‐smooth) boundary, the Zaremba (mixed boundary conditions) problem and discrete Laplacians.     

REGULARITY THEORY FOR SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS WITHN EUMANN BOUNDARY CONDITIONS

Inroductlonu consider here a system     

Mathematical problems of the theory of elasticity of chiral materials for Lipschitz domains

By the potential method, we investigate the Dirichlet and Neumann boundary value problems of the elasticity theory of hemitropic (chiral) materials in the case of Lipschitz domains. We study properties of the single‐ and double‐layer potentials and of certain, generated by them, boundary integral operators. These results are applied to reduce the boundary value problems to the equivalent first and the second kind integral equations and the uniqueness and existence theorems are proved in various function spaces. Copyright © 2005 John Wiley & Sons, Ltd.     

Weak KAM theorem for Hamilton‐Jacobi equations with Neumann boundary conditions on noncompact manifolds

In this paper, we consider Hamilton–Jacobi equations with homogeneous Neumann boundary condition. We establish some results on noncompact manifold with homogeneous Neumann boundary conditions in view of weak Kolmogorov‐Arnold‐Moser (KAM) theory, which is a generalization of the results obtained by Fathi under the non‐bounded condition. Copyright © 2014 John Wiley & Sons, Ltd.     

Comparison results for parabolic differential equations at resonance

The objective of this paper is to develop systematically general comparison techniques for semilinear parabolic equations with periodic and homogeneous Neumann boundary conditions. These results are expected to play a significant role in the existence theory for parabolic boundary value problems at resonance.     

ON THE EXISTENCE OF POSITIVE SOLUTIONS FOR SINGULAR NEUMANN BOUNDARY VALUE PROBLEMS

By using fixed point index theory, we consider the existence of positive solutions for singular nonlinear Neumann boundary value problems. Our main results extend and improve many known results even for non-singular cases.     

Boundary integral equations in time-dependent bending of thermoelastic plates

The initial-boundary value problems with the Dirichlet and Neumann boundary conditions arising in the theory of bending of thermoelastic plates with transverse shear deformation are reduced to time-dependent boundary integral equations by means of layer potentials. The solvability of these equations is then investigated in Sobolev-type spaces.     

The direct method in time-dependent bending of thermoelastic plates

The initial-boundary value problems with Dirichlet and Neumann boundary conditions arising in the theory of bending of thermoelastic plates with transverse shear deformation are reduced to time-dependent boundary integral equations by means of the Somigliana representation formulas. The solvability of these equations is then investigated in Sobolev-type spaces.