A priori estimates, existence and Liouville theorems for semilinear elliptic systems with power nonlinearities

被引：8

作者：

Quittner, Pavol ^{[1
]}

机构：

[1] Comenius Univ, Dept Appl Math & Stat, Bratislava 84248, Slovakia

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2014年 / 102卷

关键词：

Elliptic systems; A priori estimates; Liouville-type theorems; POSITIVE SOLUTIONS; WEAK SOLUTIONS; NONEXISTENCE; BOUNDEDNESS; EQUATIONS;

D O I：

10.1016/j.na.2014.02.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a priori estimates and existence of positive solutions of semilinear elliptic systems with power nonlinearities and homogeneous Dirichlet boundary conditions. In general, our systems are nonvariational and noncooperative, and our estimates are optimal in the class of very weak solutions. We also provide new Liouville-type theorems. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：144 / 158

页数：15

共 36 条

[1]

[Anonymous], 1993, Revista Matemtica Universidad Complutense de Madrid

[2]

[Anonymous], 1996, DIFFER INTEGRAL EQU

[3] Nonexistence of Positive Supersolutions of Elliptic Equations via the Maximum Principle [J].

Armstrong, Scott N. ;

Sirakov, Boyan .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2011, 36 (11) :2011-2047

[4]

Bidaut-V?ron M-F., 2002, ADV DIFFERENTIAL EQU, V7, P257

[5]

Bidaut-Veron M.-F., 2000, ADV DIFFERENTIAL EQU, V5, P147

[6]

Bidaut-Veron MF, 2010, ADV DIFFERENTIAL EQU, V15, P1033

[7] Nonexistence results and estimates for some nonlinear elliptic problems [J].

Bidaut-Véron, MF ;

Pohozaev, S .

JOURNAL D ANALYSE MATHEMATIQUE, 2001, 84 (1) :1-49

[8]

Bidaut-Véron MF, 2000, REV MAT IBEROAM, V16, P477

[9] On positive weak solutions for a class of quasilinear elliptic systems [J].

Chen, CS .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 62 (04) :751-756

[10] POSITIVE SOLUTIONS OF SEMILINEAR ELLIPTIC-SYSTEMS [J].

CLEMENT, P ;

DEFIGUEIREDO, DG ;

MITIDIERI, E .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1992, 17 (5-6) :923-940

← 1 2 3 4 →