Fredholm alternative for the p-Laplacian in higher dimensions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:263

Article

Drábek, P ; Holubová, G

关键词: p-Laplacian;    Fredholm alternative;    Leray-Schauder degree;    upper and lower solutions;    saddle point theorem;    Palais-Smale condition;   

DOI  :  10.1006/jmaa.2001.7608

来源: Elsevier

【 摘 要 】

In this paper we characterize the set of all right-hand sides h epsilon C(<()over bar>) for which the boundary value problem Delta (p)u+lambda (1)\u \ (p-2)u = h in Omega, u = 0 on partial derivative Omega has at least one weak solution u epsilon W-0(1,p)(Omega). Here 1 < p < 2, and lambda (1) > 0 is the first eigenvalue of the p-Laplacian. In particular, we prove that for f(Omega)h phi (1) = 0 this problem is solvable and the energy functional E-h(u) = 1/p integral (Omega)\ del (u)\ (p) - lambda1/p integral (Omega)\u \ (p) + integral (Omega)hu is unbounded from below. (C) 2001 Academic Press.

【 授权许可】

Free