Symmetry of solutions of some semilinear elliptic equations with singular nonlinearities

被引：34
作者：
Canino, A. [1 ]
Grandinetti, M. [1 ]
Sciunzi, B. [1 ]
机构：
[1] UNICAL, Dipartimento Matemat, I-87036 Cosenza, Italy
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2013年 / 255卷 / 12期
关键词：
Singular semilinear equations; Symmetry of solutions; Moving plane method; ASYMPTOTIC SYMMETRY; POSITIVE SOLUTIONS; CLASSIFICATION; EXISTENCE; BEHAVIOR;
D O I：
10.1016/j.jde.2013.08.014
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider positive solutions to the singular semilinear elliptic equation -Delta u = 1/u(gamma) + f (u), in bounded smooth domains, with zero Dirichlet boundary conditions. We provide some weak and strong maximum principles for the H-0(1)(Omega) part of the solution (the solution u generally does not belong to H-0(1)(Omega)), that allow to deduce symmetry and monotonicity properties of solutions, via the Moving Plane Method. (C) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码：4437 / 4447
页数：11
相关论文
共 24 条
[1]  
[Anonymous], PREPRINT
[2]  
[Anonymous], 2015, Elliptic Partial Differential Equations of Second Order. Classics in Mathematics
[3]  
Berestycki H., 1991, Bol. Soc. Bras. Mat, V22, P1, DOI DOI 10.1007/BF01244896
[4]   A Dirichlet problem with singular and supercritical nonlinearities [J].
Boccardo, Lucio .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (12) :4436-4440
[5]   Semilinear elliptic equations with singular nonlinearities [J].
Boccardo, Lucio ;
Orsina, Luigi .
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2010, 37 (3-4) :363-380
[6]   ASYMPTOTIC SYMMETRY AND LOCAL BEHAVIOR OF SEMILINEAR ELLIPTIC-EQUATIONS WITH CRITICAL SOBOLEV GROWTH [J].
CAFFARELLI, LA ;
GIDAS, B ;
SPRUCK, J .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1989, 42 (03) :271-297
[7]   Minimax methods for singular elliptic equations with an application to a jumping problem [J].
Canino, A .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 221 (01) :210-223
[8]  
Canino A, 2004, J CONVEX ANAL, V11, P147
[9]   Monotonicity of solutions of Fully nonlinear uniformly elliptic equations in the half-plane [J].
Charro, F. ;
Montoro, L. ;
Sciunzi, B. .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 251 (06) :1562-1579
[10]   CLASSIFICATION OF SOLUTIONS OF SOME NONLINEAR ELLIPTIC-EQUATIONS [J].
CHEN, WX ;
LI, CM .
DUKE MATHEMATICAL JOURNAL, 1991, 63 (03) :615-622
123