THE EXISTENCES OF POSITIVE SOLUTIONS FOR P-MEAN CURVATURE OPERATOR WITH SUPERCRITICAL POTENTIAL

• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 关键词: Mean curvature operator Mountain Pass Principle (PS) condition Ekeland's variational principle.
• 年，卷（期）: 2005,（3）
• 页码范围: 193-205
• 页数: 13页
• 分类号: O175.25.
• 语种: 英文

摘要

This paper is concerned with the existences of positive solutions of the following Dirichlet problem for p-mean curvature operator with supercritical potential: {-div((1+｜( )u｜2)p-2/2( u)=λur-1+μμq-1/｜x｜,u＞0 x∈Ω,u=0 x∈( )Ωwhere u ∈W01,p(Ω), Ω is a bounded domain in RN(N ＞ p ＞ 1) with smooth boundary ( )Ω and 0 ∈ Ω, 0 ＜ q ＜p, 0≤ s ＜ N/P(p-q)+q, p≤ r＜p*, p*=Np/N-p, μ＞0. It reaches the conclusion where this problem has two positive solutions in the different cases. It discusses the existences of positive solutions of the Dirichlet problem for the p-mean curvature operator with supercritical potential firstly. Meanwhile, it extends some results of the p-Laplace operator to that of p-mean curvature operator for p≥ 2.