QUALITATIVE ANALYSIS OF SOLUTIONS FOR A CLASS OF ANISOTROPIC ELLIPTIC EQUATIONS WITH VARIABLE EXPONENT

被引：10

作者：

Afrouzi, G. A. ^{[1
]}

Mirzapour, M. ^{[1
]}

Radulescu, Vicentiu D. ^{[2
,3
]}

机构：

[1] Univ Mazandaran, Fac Math Sci, Dept Math, Babol Sar, Iran

[2] King Abdulaziz Univ, Fac Sci, Dept Math, Jeddah, Saudi Arabia

[3] Romanian Acad, Inst Math Simion Stoilow, POB 1-764, Bucharest 014700, Romania

来源：

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2016年 / 59卷 / 03期

关键词：

degenerate anisotropic Sobolev spaces; variable exponent; Dirichlet boundary value condition; fountain theorem; Ekeland variational principle; SPACES; MULTIPLICITY; EXISTENCE;

D O I：

10.1017/S0013091515000346

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We are concerned with the degenerate anisotropic problem - [GRAPHICS] partial derivative(xi) a(i) (x, partial derivative(xi) u) + b(x) vertical bar u vertical bar (P)(+-2)(+) u = f(x, u) in Omega, u = 0 on partial derivative Omega. We first establish the existence of an unbounded sequence of weak solutions. We also obtain the existence of a non-trivial weak solution if the nonlinear term f has a special form. The proofs rely on the fountain theorem and Ekeland's variational principle.

引用

页码：541 / 557

页数：17

共 27 条

[1] Ambrosetti A., 1973, Journal of Functional Analysis, V14, P349, DOI 10.1016/0022-1236(73)90051-7
[2] [Anonymous], 2002, Electrorheological Fluids: Modeling and Mathematical Theory
[3] [Anonymous], 2002, THESIS U FRIEBURG GE
[4] [Anonymous], 1997, Minimax theorems
[5] INFINITELY MANY SOLUTIONS OF A SYMMETRICAL DIRICHLET PROBLEM
BARTSCH, T
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1993, 20 (10) : 1205 - 1216
[6] Multiplicity of solutions for a class of anisotropic elliptic equations with variable exponent
Boureanu, Maria-Magdalena
Pucci, Patrizia
Radulescu, Vicentiu D.
[J]. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2011, 56 (7-9) : 755 - 767
[7] INFINITELY MANY SOLUTIONS FOR A CLASS OF DEGENERATE ANISOTROPIC ELLIPTIC PROBLEMS WITH VARIABLE EXPONENT
Boureanu, Maria-Magdalena
[J]. TAIWANESE JOURNAL OF MATHEMATICS, 2011, 15 (05): : 2291 - 2310
[8] Variable exponent, linear growth functionals in image restoration
Chen, Yunmei
Levine, Stacey
Rao, Murali
[J]. SIAM JOURNAL ON APPLIED MATHEMATICS, 2006, 66 (04) : 1383 - 1406
[9] Diening L., 2004, FSDONA04 Proc, V66, P38
[10] VARIATIONAL PRINCIPLE
EKELAND, I
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1974, 47 (02) : 324 - 353

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