跳跃非线性条件下椭圆边值问题的变号解和多解存在性

本文应用Banach空间常微分方程和极大极小理论,特别是相对山路引理研究了零点和无穷远点跳跃非线性条件下椭圆边值问题的变号解和多解,得到新的变号解和多解存在性定理,最后我们得到6个非平凡解的存在性.     

跳跃非线性条件下椭圆边值问题的变号解和多解存在性

本文应用Ｂａｎａｃｈ空间常微分方程和极大极小理论,特别是相对山路引理研究了零点和无穷远点跳跃非线性条件下椭圆边值问题的变号解和多解,得到新的变号解和多解存在性定理,最后我们得到６个非平凡解的存在性．     

一个带限制的椭圆特征问题的多解和变号解

利用变分方法证明了一个带限制的半线性椭圆特征问题变号解的存在性.所获得的3个解,1个是正解、1个是负解、1个是变号解.在某些附加条件下证明了多重变号解的存在性.     

具有变号非线性项的拟线性椭圆方程多解的存在性

利用山路定理研究了具有Dirichlet边值问题-div(|▽u|~(2p-2)▽u/(1+|▽u|~(2p))~(1/2))=λf(x,u)多解的存在性,且非线性项f可以变号.     

一类临界增长非线性椭圆方程的解

利用非光滑临界点理论 ,本文证明了一类临界增长非线性椭圆方程-div(A(x ,u) ｜ u｜p-2 u) 1pA′u(x ,u) ｜ u｜p =g(x ,u) ｜u｜p -2 u ,u=0 ,　 Ω ; Ω 非平凡正解的存在性 .其中 1 相似文献   

一类周期变号的非线性Schroedinger方程解的存在性

讨论非线性Schroedinger方程-△u q（x）u=λu Q（x）│u│^p-1u x∈R^N的解的存在性,其中q(x),Q(x)满足周期性条件,而且Q（x)变号,λ∈R落在-△ q的谱隙中,1＜p＜N 2/N-2。     

四阶方程两点边值问题变号解的存在性

利用一个已有的抽象结论,证明了一类非线性四阶方程两点边值问题变号解的存在性.     

零点有次线性项的椭圆问题的变号解

Abstract. It is proved that the semilinear elliptic problem with zero boundary value     

一类非线性椭圆方程解的存在性

本文考虑一类非线性椭圆方程,运用强制变分方法,我们给出了在多种情况下方程解的存在性。     

一类含临界指数双调和方程变号解的存在性

本文运用一个新的环绕定理讨论了一类含临界指数双调和方程分别在Navier和Dirichlet边界下变号解的存在性.     

Strong Solution of the Obstacle Problem for Fully Nonlinear Elliptic Equations

In this paper we obtain the existence of W^{2, ∞} solutions of the obstacle problems for fully nonlinear elliptic equations under more general structure conditions than those in [1] by using the mollifier approach, which is also extended in our discussion.     

Multiple Sign-Changing Solutions for Quasilinear Equations of Bounded Quasilinearity

The existence of an infinite sequence of sign-changing solutions are proved for a class of quasilinear elliptic equations under suitable conditions on the quasilinear coefficients and the nonlinearity■ where ? ? R~N is a bounded domain with smooth boundary, and we use■ The main interest of this paper is for the case of bounded quasilinearity bij. The result is proved by an elliptic regularization method involving truncations of both u and the gradient of u.     

Superlinear Fourth-Order Elliptic Problem Without Ambrosetti and Rabinowitz Growth Condition

This paper deals with superlinear fourth-order elliptic problem under Navier boundary condition. By using the mountain pass theorem and suitable truncation, a multiplicity result is established for all $λ > 0$ and some previous result is extended.     

Existence and Regularity of Solutions of a Nonlinear Nonuniformly Elliptic System Arising from a Thermistor Problem

A thermistor is an electric circuit device made of ceramic material whose electric conductivity depends on the temperature. If the only heat source is the electric heating, the temperature and the electric potential satisfy a nonlinear elliptic system which is also degenerate if the electric conductivity is not uniformly bounded from above or away from zero. Under general boundary conditions, we establish existence and Hölder continuity of solutions of such a nonlinear nonuniformly elliptic system. When the elechic conductivity linearly depends on the temperature, we provide a non-uniqueness and non-existence example.     

Sign-Changing Solutions for a Class of Nonlinear Elliptic Problems

In the present paper,the author studies the existence of sign-changing solutions for nonlinear elliptic equations,which have jumping nonlinearities,and may or may not be resonant with respect to Fu(?)ik spectrum,via linking methods under Cerami condition.     

一类非线性人口问题的渐近解

本研究了一类非线奇摄动人口问题.在适当的条件下,首先求出了原问题的外部解,然后利用伸长变量和幂级数展开理论构造出解的形式渐近展开式.最后利用微分不等式理论,讨论了问题解的-致有效性.     

四阶椭圆型方程奇异摄动问题的数值解

本文对一类四阶椭圆型方程奇异摄动问题建立了指数型拟合差分格式,并且证明了这种格式在能量范数意义下关于小参数ε的一致收敛性.最后,我们给出了数值结果.     

非线性三点边值问题正解的存在性

本利用锥上的不动点定理,在f满足超线性条件或次线性条件下,讨论了边值问题u^n a(t)f(u)=0,r∈(0,1)u′(0)=0,u(1)=au(η）正确的存在性。