一类拟线性奇异椭圆方程无穷多解的存在性  

EXISTENCE OF INFINITELY MANY SOLUTIONS FOR SOME QUASILINEAR SINGULAR ELLIPTIC EQUATION

作　　者：龚亚英[1] 

机构地区：[1]重庆三峡职业学院基础部,重庆万州404000

出　　处：《数学杂志》2010年第4期726-730,共5页Journal of Mathematics

摘　　要：本文研究有界区域ΩR^N上拟线性奇异椭圆方程.利用变分法,在f满足非二次条件的情况下,运用对偶喷泉定理证明了存在λ~*>0使得当λ∈(0,λ~*)时,该方程存在无穷多个具有负能量的弱解{u_k}.推广了s=0时的相应结果.In this article,we consider the following quasilinear singular elliptic equation. By using the variational methods,if f satisfies nonquadratic condition,via dual fountain theorem, we prove that there existsλ^〉0 such that for anyλ∈（0,λ^＊）,this problem has a sequence of solutions {uk} belong to  W0^1,p（Ω） such that I（uk）0 and I（uk）→0 as k→＋∞,which generalize the results of the case s = 0.

关 键 词：SOBOLEV-HARDY临界指数 拟线性椭圆方程 (PS)_c~*条件 对偶喷泉定理 非二次条件 

分 类 号：O175.25[理学—数学]