A MIN-MAX PRINCIPLE FOR NON-DIFFERENTIABLE FUNCTIONS WITH A WEAK COMPACTNESS CONDITION

被引：9

作者：

Livrea, Roberto ^{[1
]}

Marano, Salvatore A. ^{[2
]}

机构：

[1] Univ Mediterranea Reggio Calabria, Dipartimento PAU, I-89100 Reggio Di Calabria, Italy

[2] Univ Catania, Dipartimento Matemat & Informat, I-95125 Catania, Italy

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2009年 / 8卷 / 03期

关键词：

Critical points; locally Lipshitz continuous functions; weak Palais-Smale condition; Mountain Pass geometry; CRITICAL-POINT THEORY; EQUATIONS; THEOREMS;

D O I：

10.3934/cpaa.2009.8.1019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A general critical point result established by Ghoussoub is extended to the case of locally Lipschitz continuous functions satisfying a weak Palais-Smale hypothesis, which includes the so-called non-smooth Cerami condition. Some special cases are then pointed out.

引用

页码：1019 / 1029

页数：11

共 22 条

[1]

[Anonymous], 1990, CLASSICS APPL MATH

[2]

[Anonymous], 1999, NONCONVEX OPTIM APPL

[3]

BONANNO G, STRUCTURE CRITICAL S

[4] VARIATIONAL-METHODS FOR NON-DIFFERENTIABLE FUNCTIONALS AND THEIR APPLICATIONS TO PARTIAL-DIFFERENTIAL EQUATIONS [J].

CHANG, KC .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1981, 80 (01) :102-129

[5] Quantitative deformation theorems and critical point theory [J].

Corvellec, JN .

PACIFIC JOURNAL OF MATHEMATICS, 1999, 187 (02) :263-279

[6] NON-CONVEX MINIMIZATION PROBLEMS [J].

EKELAND, I .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1979, 1 (03) :443-474

[7]

EKELAND I, 1990, ERGEB MATH GRENZBEB, V19

[8] Critical point theorems and applications to differential equations [J].

El Amrouss, AR .

ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2005, 21 (01) :129-142

[9]

GASINSKI L, 2005, SER MATH APPL, V8

[10] A GENERAL MOUNTAIN PASS PRINCIPLE FOR LOCATING AND CLASSIFYING CRITICAL-POINTS [J].

GHOUSSOUB, N ;

PREISS, D .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1989, 6 (05) :321-330

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