On a Liouville-type equation with sign-changing weight

被引：1

作者：

Ruf, Bernhard ^{[1
]}

Ubilla, Pedro ^{[2
]}

机构：

[1] Univ Milan, Dipartimento Matemat, I-20133 Milan, Italy

[2] Univ Santiago Chile, Dept Matemat & CC, Santiago, Chile

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2009年 / 139卷

关键词：

2-DIMENSIONAL EULER EQUATIONS; STATISTICAL-MECHANICS; LOCAL SUPERLINEARITY; STATIONARY FLOWS; EXISTENCE; BLOW;

D O I：

10.1017/S0308210507000583

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the existence, nonexistence and multiplicity of non-negative solutions for the family of problems -Delta u = lambda(a(x)eu + f(x, u)), u is an element of H-0(1) (Omega), where Omega is a bounded domain in R-2 and lambda > 0 is a parameter. The coefficient a(x) is permitted to change sign. The techniques used in the proofs are a combination of upper and lower solutions, the Trudinger-Moser inequality and variational methods. Note that when f(x, u) = 0 the equation is of Liouville type.

引用

页码：183 / 192

页数：10

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