关键词: 弱解, 临界指数, (PS) 条件, 山路引理

Abstract:

The existence of the nontrivial solution of a weighted generalized mean curvature-div((1+I ▽uI ²)^p-2/2▽u)=λIuI ^r-2u+μ|u|^q-2/|x|^su in some c0nditions,such as the Dirichlet boundary c0nditi0n and the condition that r and q are less than the critical exponent,is investigated in this paper. In the investigation,the Sobolev-Hardy ine.quality,the theorem of almost everywhere convergence of the gradient u_n and the Mountain Pass Lemma Satisfying the(PS)_c conditions are adopted.Thus,the dificulties in verifying the Mountain Pass geometric conditions and the PS conditions are conquered.

Key words: weak solution, critical exponent, (PS)_c condition, Mountain Pass Lemma