关键词: 拟线性椭圆方程, 临界指数, 变分泛函, 山路引理, 集中紧性原理

Abstract:

In this paper, Dirichlet problemis discussed, in which ΩcR~N is a bounded domain and f(x,u)=O(|ul~(Q-2)u)(u→∞, Q=(NP)/(N-P), N>p≥2 The auther has proved that the psoblem (*) possesses a nontrivial weak solution under given conditions of a_1(x,s) and f(x,u).

Key words: Quasilinear elliptic equation, Critical exponent, Variational function, Theorem of mountain path, Concentration-compactness principle