Nehari manifold and existence of positive solutions to a class of quasilinear problems

被引：61

作者：

Alves, CO ^{[1
]}

El Hamidi, A

机构：

[1] Univ Fed Campina Grande, Dept Matemat & Estat, BR-58109970 Campina Grande, PB, Brazil

[2] Univ Rochelle, Lab Math & Applicat, F-17042 La Rochelle, France

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2005年 / 60卷 / 04期

关键词：

variational method; quasilinear problem; critical Sobolev exponent;

D O I：

10.1016/j.na.2004.09.039

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, existence and multiplicity results to the following nonlinear elliptic equation: -Delta(p)u = lambda\u\(q-2)u + \u\(p*-2)u, u > 0 in Omega subset of R-N, together with mixed Dirichlet-Neumann or Neumann boundary conditions, are established. Here, Delta(p)u denotes the p-Laplacian operator, 1 < q < p < N, p* = Np/(N - p) and lambda is a positive real parameter. The study is based on the extraction of Palais-Smale sequences in the Nehari manifold. (C) 2004 Elsevier Ltd. All rights reserved.

引用

页码：611 / 624

页数：14

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