一类椭圆混合边值问题无穷多解的存在性  

Existence Results of Infinitely Solutions to Elliptic Mixed Boundary Value Problem

作　　者：李国发[1] 刘海鸿[2] 

机构地区：[1]曲靖师范学院数学与信息科学学院,云南曲靖655011 [2]云南师范大学数学学院,云南昆明650092

出　　处：《四川师范大学学报（自然科学版）》2013年第2期233-235,共3页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金天元基金(10926167)资助项目

摘　　要：研究了一类新的椭圆混合边值问题,该问题中的变元u必须同时满足内部及边界的要求.假设非线性项f(x,u)关于u在无穷远处满足超线性、次临界增长且是奇的,利用对称山路定理证明了该边值问题在一带孔的空心区域上存在无穷多对弱解.另外,还讨论了迹定理、Sobolev嵌入定理在该椭圆混合边值问题中的应用,几个嵌入不等式被用于弱解存在性定理的证明.A new elliptic mixed boundary value problem is studied. The variable u of the boundary value problem must satisfy in- ner and boundary condition. Assume that the nonlinear term f（x, u） is superlinear with respect to u at infinity, sub - critical growth and odd, the existence results of infinitely weak solutions in a bounded domain with holes are proved by Symmetric Mountain Pass Theorem. Furthermore, trace theorem and Sobolev embedding theorem are discussed for the mixed boundary value problem. Some embed- ding inequalities are applied to the proof of the existence of weak solutions.

关 键 词：临界点理论 椭圆方程 对称山路定理 超线性 嵌入定理 

分 类 号：O176.3[理学—数学]