ON COMPACTNESS CONDITIONS FOR THE p-LAPLACIAN

被引：0

作者：

Jirasek, Pavel ^{[1
]}

机构：

[1] Univ W Bohemia, Dept Math, Univ 8, Plzen 30614, Czech Republic

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2016年 / 15卷 / 03期

关键词：

Boundary value problems; variational methods; Palais-Smale condition; p-Laplacian; Fredholm alternative;

D O I：

10.3934/cpaa.2016.15.715

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the geometry and validity of various compactness conditions (e.g. Palais-Smale condition) for the energy functional J(lambda 1) (u) = 1/p integral(Omega) vertical bar del u vertical bar(p) dx - lambda 1/p integral(Omega) vertical bar u vertical bar(p) dx - integral(Omega) dx for u is an element of W-0(1,p)(Omega) 1 < p < infinity, where Omega is a bounded domain in R-N, f is an element of L-infinity(Omega) is a given function and -lambda(1) < 0 is the first eigenvalue of the Dirichlet p-Laplacian Delta(p) on W-0(1,p)(Omega).

引用

页码：715 / 726

页数：12