Nonexistence of positive supersolutions to some nonlinear elliptic problems

被引：20

作者：

Alarcon, S. ^{[1
]}

Garcia-Melian, J. ^{[2
,3
]}

Quaas, A. ^{[1
]}

机构：

[1] Univ Tecn Federico Santa Maria, Dept Matemat, Valparaiso, Chile

[2] Univ La Laguna, Dept Anal Matemat, San Cristobal la Laguna 38271, Spain

[3] Univ La Laguna, Fac Fis, Inst Univ Estudios Avanzados IUdEA Fis Atam Mol &, San Cristobal la Laguna 38203, Spain

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2013年 / 99卷 / 05期

关键词：

Nonlinear elliptic problems; Liouville type theorems; Comparison principle; LIOUVILLE-TYPE THEOREMS; EQUATIONS; EXISTENCE; BEHAVIOR;

D O I：

10.1016/j.matpur.2012.10.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we obtain Liouville type theorems for positive supersolutions of the elliptic problem -Delta u + vertical bar del u vertical bar(q) = lambda f(u) in exterior domains of R-N. Here q > 1 and the function f can be compared with a power p near zero or infinity. We show that positive supersolutions do not exist in some ranges of the parameters p and q which turn out to be optimal for the model case f(s) = s(p). The related problem -Delta u - vertical bar del u vertical bar(q) = f(u) is also analyzed. (C) 2012 Elsevier Masson SAS. All rights reserved.

引用

页码：618 / 634

页数：17