一类超二次退化椭圆方程非平凡解的存在性  

Existence of nontrivial solutions for a class of superquadratic degenerate elliptic equations

作　　者：安育成[1] 索洪敏[2] 

机构地区：[1]毕节学院理学院,贵州毕节551700 [2]贵州民族大学理学院,贵州贵阳550025

出　　处：《辽宁工程技术大学学报（自然科学版）》2014年第9期1284-1288,共5页Journal of Liaoning Technical University (Natural Science)

基　　金：贵州省科技厅联合基金资助项目(LKB[2012]19);贵州省科学技术基金资助项目([2013]2141);国家自然科学基金资助项目(11361003)

摘　　要：为获得退化椭圆方程在超二次条件下非平凡解的存在性,利用紧自伴算子的谱理论,研究退化椭圆方程对应特征值问题,给出特征值和对应的特征函数的性态;根据微分方程中的变分方法,建立退化椭圆方程对应的变分结构,利用临界点理论中的局部环绕定理,获得了一些新的可解性条件,统一和推广了已有文献的一些结果.In order to obtain existence of nontrivial solutions for a class of superquadratic degenerate elliptic equations, this paper firstly studied the corresponding eigenvalue problem by using the spectral theory for compact operator, and then established the eigenvalue and the characteristic of eigenfunction. Secondly, by using variational method in differential equation, the corresponding variational structure is established. Finally, some new solvability conditions are obtained for the degenerate elliptic equation by the local linking theorem in critical point theory, and some of the recent corresponding results were improved and generalized.

关 键 词：退化椭圆方程 变分方法 局部环绕定理 超二次条件 非平凡解 

分 类 号：O175.25[理学—数学]