摘要
利用没有PS条件的山路引理 ,研究了以下问题在一定条件下的弱正解的存在性 :-div( u p- 2 u) +a(x)up- 1 =h(x)uq+up - 1 ,x∈RN,u≥ 0 ,u≠ 0 ,∫RNa(x)u pdx <+∞ .其中a :RN →R是连续非负函数 ,h∶RN →R是某类可积函数 .2 ≤ p<N且p2 ≤N ,p- 1 <q <p - 1 ,p =NpN - p.从而在较弱的条件下推广了
This paper is concerned with the following nonlinear Dirichlet problem by the Mountain Pass principle without Palais Smale condition:-\%div\%(u p-2 u) + a(x) u p-1 = h(x) u q+u p *-1 , x∈R N, u≥0, u≠0, ∫ R N a(x) u p\%d\%x <+∞. Where a:R N→R is continuous and nonnegative,h:R N→R is some integrable function and 2≤p<N, p 2≤N , p-1<q<p *-1 ,p *=NpN-p. Some results as p=2 are generalized at weakly conditions.
基金
国家自然科学基金 ( 10 1710 3 2 )
广东省自然科学基金 ( 0 1160 6)资助项目
关键词
临界指数
集中紧原理
山路引理
椭圆型方程
critical Sobolev exponent
concentration compactness principle
Mountain Pass Principle
elliptic equations
