EXISTENCE OF SOLUTIONS FOR A CLASS OF p(x)-LAPLACIAN EQUATIONS INVOLVING A CONCAVE-CONVEX NONLINEARITY WITH CRITICAL GROWTH IN RN

被引：39

作者：

Alves, Claudianor O. ^{[1
]}

Ferreira, Marcelo C. ^{[1
]}

机构：

[1] Univ Fed Campina Grande, Unidade Acad Matemat, BR-58429900 Campina Grande, PB, Brazil

来源：

TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS | 2015年 / 45卷 / 02期

关键词：

Variational Methods; p(x)-Laplacian; critical growth; MULTIPLE SOLUTIONS; POSITIVE SOLUTIONS; ELLIPTIC EQUATION; VARIABLE EXPONENT; SPACES; THEOREMS;

D O I：

10.12775/TMNA.2015.020

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the existence of solutions for a class of quasilinear problems involving variable exponents and with nonlinearity having critical growth. The main tool used is the variational method, more precisely, Eke land's Variational Principle and the Mountain Pass Theorem.

引用

页码：399 / 422

页数：24

共 40 条

[1] Regularity results for electrorheological fluids: the stationary case [J].

Acerbi, E ;

Mingione, G .

COMPTES RENDUS MATHEMATIQUE, 2002, 334 (09) :817-822

[2] Regularity results for stationary electro-rheological fluids [J].

Acerbi, E ;

Mingione, G .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2002, 164 (03) :213-259

[3] Existence of solution for a degenerate p(x)-Laplacian equation in RN [J].

Alves, Claudianor O. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 345 (02) :731-742

[4] Nonlinear perturbations of a p(x)-Laplacian equation with critical growth in RN [J].

Alves, Claudianor O. ;

Ferreira, Marcelo C. .

MATHEMATISCHE NACHRICHTEN, 2014, 287 (8-9) :849-868

[5]

Alves CO, 2010, DIFFER INTEGRAL EQU, V23, P113

[6]

Alves CO, 2006, PROG NONLINEAR DIFFE, V66, P17

[7] Existence of positive solutions for a problem with lack of compactness involving the p-Laplacian [J].

Alves, CO .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2002, 51 (07) :1187-1206

[8] COMBINED EFFECTS OF CONCAVE AND CONVEX NONLINEARITIES IN SOME ELLIPTIC PROBLEMS [J].

AMBROSETTI, A ;

BREZIS, H ;

CERAMI, G .

JOURNAL OF FUNCTIONAL ANALYSIS, 1994, 122 (02) :519-543

[9]

[Anonymous], [No title captured]

[10]

[Anonymous], 1983, LECT NOTES MATH

← 1 2 3 4 →