数学物理学报(英文版)
數學物理學報(英文版)
수학물이학보(영문판)
Acta Mathematica Scientia
2004年
3期
395-402
,共8页
critical Sobolev exponent%concentration compactness principle%genus%in-finitely many solutions
This paper is concerned with the following nonlinear Dirichlet problem:{-△pu =|u|p*- 2u + λf(x,u)x ∈Ω, u =0x ∈(e)Ω, where △pu=div(|(△)u|p-2(△)u) is the p-Laplacian of u,Ω is a bounded domain in Rn(n≥3),1 ＜ p ＜ n,p·=pn/n-p is the critical exponent for the Sobolev imbedding,λ＞ 0 and f(x, u)satisfies some conditions. It reaches the conclusion that this problem has infinitely many solutions.Some results as p = 2 or f(x, u) = |u|q- 2u, where 1 ＜ q ＜ p,are generalized.
