非线性本征值问题的正解  

Positive Solutions of Nonlinear Eigenvalue Problems

作　　者：艾军[1] 朱熹平[1] 

机构地区：[1]中山大学数学系

出　　处：《中山大学学报（自然科学版）》1989年第1期11-16,共6页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：中山大学高等学术研究中心基金会资助项目

摘　　要：研究一类非线性椭圆型方程的本征值问题,在非线性项可以临界增长的条件下证明其正解的存在性,并在适当条件下证明了这类本征值问题至少存在两个正解。This paper is concerned with the existence of positive solutions for a class of semilinear elliptic eigenvalue problems involving critical Sobolev exponents. Under the assumption given in the paper for the nonlinear terms f(u), we proved that there exists a finite number λ~*>0, such that, there is a minimum positive solution for the eigenvalue problem when 0<λ<λ~*, there is no positivs solution for the eigenvalue problem when λ>λ~*. If f(u) is a convex function, there exists at least another positive solution for the eigenvalue problem when 0<λ<λ~*.

关 键 词：本征值问题 正解 变分方法 

分 类 号：O175.9[理学—数学]