A critical point theorem via the Ekeland variational principle

被引：210

作者：

Bonanno, Gabriele ^{[1
]}

机构：

[1] Univ Messina, Dept Sci Engn & Architecture, Math Sect, Fac Engn, I-98166 Messina, Italy

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2012年 / 75卷 / 05期

关键词：

Critical point; Variational methods; Palais-Smale condition; Local minimum; Multiple critical points; FUNCTIONALS;

D O I：

10.1016/j.na.2011.12.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to establish the existence of a local minimum for a continuously Gateaux differentiable function, possibly unbounded from below, without requiring any weak continuity assumption. Several special cases are also emphasized. Moreover, a novel definition of Palais-Smale condition, which is more general than the usual one, is presented and a mountain pass theorem is pointed out. As a consequence, multiple critical points theorems are then established. Finally, as an example of applications, an elliptic Dirichlet problem with critical exponent is investigated. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：2992 / 3007

页数：16