带临界指数的奇异椭圆方程Neumann问题多重解的存在性  

Existence of multiple solutions for singular elliptic equations involving critical exponents with Neumann boundary condition

作　　者：陈自高[1] 

机构地区：[1]华北水利水电学院数学与信息科学学院,郑州450011

出　　处：《华东师范大学学报（自然科学版）》2011年第5期79-87,共9页Journal of East China Normal University(Natural Science)

基　　金：河南省科技厅自然科学基金(102102210216);河南省教育厅自然科学基金(2010A110012)

摘　　要：利用变分法,在n维空间有界区域Ω上,研究了一类含有Sobolev-Hardy临界指数与Hardy项的奇异椭圆方程Neumann问题弱解的存在性和多重性.在f(x,t)满足非二次条件的情况下,运用对偶喷泉定理与拉直边界的方法,证明了存在λ~*>0使得当λ∈(0,λ~*)时,该问题存在无穷多个具有负能量的弱解{u_k}E^(1,2)(Ω),并且当k→∞时,J(u_k)→0.By using variational methods,the existence and multiplicity of weak solutions for Neumann boundary problem for some singular elliptic equations involving critical Sobolev-Hardy exponents and Hardy terms was studied on bounded domainΩR^N.If f（x,t） satisfies the non-quadratic condition,based on the dual fountain theorem and the means of straightening the boundary,we proved that there existsλ~＊0 such that for anyλ∈（0,λ~＊）,this problem has a sequence of solutions {u_k} W^（1,2）（Ω） such that J{u_k）0 and J{u_k）→0 as k→∞.

关 键 词：NEUMANN问题 SOBOLEV-HARDY临界指数 (PS)_c~＊条件 对偶喷泉定理 

分 类 号：O175.25[理学—数学]