A multiplicity theorem for the Neumann p-Laplacian with an asymmetric nonsmooth potential

We consider a nonlinear Neumann problem driven by the p-Laplacian differential operator with a nonsmooth potential (hemivariational inequality). By combining variational with degree theoretic techniques, we prove a multiplicity theorem. In the process, we also prove a result of independent interest relating and local minimizers, of a nonsmooth locally Lipschitz functional.      

Existence and Asymptotic Behavior of Boundary Blow-up Weak Solutions for Problems Involving the p-Laplacian

Let D⊂R^N(N ≥ 3), be a smooth bounded domain with smooth boundary ∂D. In this paper, the existence of boundary blow-upweak solutions for the quasilinear elliptic equation Δ_pu=λk(x) f (u) in D(λ > 0 and 1 < p < N), is obtained under new conditions on k. We give also asymptotic behavior near the boundary of such solutions.     

具有p-Laplacian算子的高阶四点边值问题多重正解的存在性

通过应用Avery-Peterson不动点定理,研究了一类具有p-Laplacian算子的高阶四点边值问题,我们得到了这类边值问题至少存在三个正解.     

具有p-Laplacian算子的二阶微分方程Picard边值问题(英文)

Suffcient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations {[φ（x（t））] ＋ kx（t） ＋ g（t,x（t）） = p（t）,t ∈（0,π） x（0） = x（π） = 0 are established,where [φ（x）] =（｜x ｜p-2x） with p 1.Our result is new even when [φ（x）] = x in above problem,i.e.p = 2.Examples are presented to illustrate the effciency of the theorem in this paper.     

由p-Laplacian算子导出的半变分不等式的特征值问题

研究了一类具有非光滑局部Lipschitz位势(半变分不等式)的非线性特征值问题其中1相似文献   

Elliptic equations with indefinite concave nonlinearities near the origin

In this note existence of infinitely many solutions is proved for an elliptic equation with indefinite concave nonlinearities.     

一类具有p-Laplacian的非线性特征值问题

利用变分法中的一个三临界点定理,在适当的假设下,研究了一类具有p-Laplacian的特征值Dirichlet问题至少存在三个弱解的充分条件.     

Optimality Criteria for Nonsmooth Continuous-Time Problems of Multiobjective Optimization

A nonsmooth multiobjective continuous-time problem is introduced. We establish the necessary and sufficient optimality conditions under generalized convexity assumptions on the functions involved. This research was supported by Center of Excellence for Mathematics, University of Isfahan, Isfahan, Iran.     

一维p-Laplacian方程正解的存在性

本文考虑一维p-Laplacian非线性边值问题(ψ(u′))′+f(t,u)=0,αψ(u(0))—βψ(u′(0))=O,γψ(u(1))+δψ(u′(1))=0,其中ψ(s):=|s|~(p-2)s,P>1.通过应用Krasnoselskii锥不动点定理,建立了该问题存在多个正解的充分条件,推广并丰富了以往文献的一些结论.     

Duality for Nonsmooth Continuous-Time Problems of Vector Optimization

We consider a nonsmooth vector optimization continuous-time problem. We establish weak and strong duality theorems under generalized convexity assumptions. This research was supported by Center of Excellence for Mathematics, University of Isfahan, Isfahan, Iran.     

一维p-Laplacian方程边值问题多解的存在性

利用Clark定理，研究了一维p-Laplacian方程边值问题多解的存在性，得到了这类边值问题至少有n对非平凡解的充分条件．     

具p-Laplacian算子型奇异边值问题的正解

考虑一类p-Laplacian算子型泛函微分方程的奇异边值问题,利用锥不动点定理,得到了其正解及多个正解存在的充分条件．     

非光滑非凸向量极值问题的真有效解

本文考虑非光滑非凸向量极值问题的真有效解,其主要结果如下:(1)Borwein真有效解与Benson真有效解的等价性;(2)向量极值问题的真有效解与标量极值问题的最优解的等价性;(3)广义鞍点定理;(4)真有效解的必要和充分条件。     

On existence of weak solutions for one-dimensional forward-backward diffusion equations

We establish the existence of infinitely many weak solutions for the general one-dimensional forward-backward diffusion equation u_t=σ(u_x)_x under the homogeneous Neumann boundary condition by rephrasing it as a first-order differential inclusion problem.     

Infinitely many positive solutions for an elliptic problem with critical or supercritical growth

We prove that for some supercritical exponents and for some smooth domains D in RN there are infinitely many (distinct) positive solutions to the following Lane–Emden–Fowler equation: This seems to be the first result for such type of equations.     

p-Laplacian方程的Aubry-Mather集

本文通过引进合适的作用-角变量变换并结合新的估计方法,对p-Laplacian方程的Poincare映射应用推广的Aubry-Mather定理,证明了一类p-Laplacian方程的Aubry-Mather集的存在性.     

一类含有p-拉普拉斯算子的二阶边值问题的单调迭代正解（英文）

研究了一类含有p-拉普拉斯算子的微分方程积分边值问题.运用迭代技巧,给出了这一类边值问题的单调正解,值得感兴趣的是微分方程中的非线性项含有一阶导数.     

与广义P-Laplace算子相关的非线性边值问题在一族空间中解的存在性

利用非线性增生映射值域的扰动定理,研究了非线性椭圆边值问题(1)在Ls(Ω)空间中解的存在性,其中max(N,2)ps< ∞.(1)-div(C(x) |u|2)p-22u |u|p-2u g(x,u(x))=fa.e.x∈Ω-〈n,(C(x) |u|2)p-22u〉∈βx(u(x))a.e.x∈Γ这里f∈Ls(Ω)给定,ΩRN为有界锥形区域,n为Γ的外法向导数,g∶Ω×R→R满足Caratheodory条件且对x∈Γ,βx是正常、凸、下半连续函数φx=φ(x,.)的次微分,其中φ∶Γ×R→R.本文是对笔者以往一些工作的继续和补充.