Existence and uniqueness for the p(x)-Laplacian-Dirichlet problems

被引：19
作者：
Fan, Xianling [1 ,2 ]
机构：
[1] Lanzhou City Univ, Dept Math, Lanzhou 730070, Peoples R China
[2] Lanzhou Univ, Dept Math, Lanzhou 730000, Peoples R China
来源：
MATHEMATISCHE NACHRICHTEN | 2011年 / 284卷 / 11-12期
基金：
中国国家自然科学基金;
关键词：
p(x)-Laplacian; uniqueness; existence; radial symmetry; LINEAR ELLIPTIC-EQUATIONS; POSITIVE SOLUTIONS; EIGENVALUE PROBLEMS; MULTIPLICITY RESULT; VARIABLE EXPONENT; RADIAL SOLUTIONS; GROUND-STATES; P-LAPLACIAN; SPACES; REGULARITY;
D O I：
10.1002/mana.200810203
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Two results on the existence and uniqueness for the p(x)-Laplacian-Dirichlet problem -div(|del u|(p(x)-2)del u) = f(x, u) in Omega, u = 0 on partial derivative Omega, are obtained. The first one deals with the case that f(x, u) is nonincreasing in u. The second one deals with the radial case in which f(r, u) is nondecreasing in u and satisfies the sub-p_ -1 growth condition. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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页码：1435 / 1445
页数：11
相关论文
共 45 条
[1]   Regularity results for a class of functionals with non-standard growth [J].
Acerbi, E ;
Mingione, G .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2001, 156 (02) :121-140
[2]   A remark on the uniqueness of positive solutions for some Dirichlet problems [J].
Afrouzi, GA ;
Rasouli, SH .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 64 (12) :2773-2777
[3]   Uniqueness and nondegeneracy for some nonlinear elliptic problems in a ball [J].
Aftalion, A ;
Pacella, F .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2003, 195 (02) :380-397
[4]  
Alves CO, 2006, PROG NONLINEAR DIFFE, V66, P17
[5]  
Antontsev S, 2006, HBK DIFF EQUAT STATI, V3, P1, DOI 10.1016/S1874-5733(06)80005-7
[6]   Radial solutions for the p-Laplacian equation [J].
Bachar, Imed ;
Ben Othman, Sonia ;
Maagli, Habib .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (06) :2198-2205
[7]   Comparison theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results [J].
Damascelli, L .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1998, 15 (04) :493-516
[8]  
DIAZ JI, 1987, CR ACAD SCI I-MATH, V305, P521
[9]  
Diening L., 2004, FSDONA04 Proc, V66, P38
[10]  
Dinu TL, 2005, SIB ELECTRON MATH RE, V2, P208
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