A Trudinger-Moser inequality in a weighted Sobolev space and applications

被引：29

作者：

Furtado, Marcelo F. ^{[1
]}

Medeiros, Everaldo S. ^{[2
]}

Severo, Uberlandio B. ^{[2
]}

机构：

[1] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF, Brazil

[2] Univ Fed Paraiba, Dept Matemat, BR-58051900 Joao Pessoa, Paraiba, Brazil

来源：

MATHEMATISCHE NACHRICHTEN | 2014年 / 287卷 / 11-12期

关键词：

Trudinger-Moser inequality; weighted Sobolev space; critical exponential growth; NONHOMOGENEOUS ELLIPTIC PROBLEM; POSITIVE SOLUTIONS; CRITICAL EXPONENT; EQUATIONS; MULTIPLICITY; EXISTENCE; GROWTH;

D O I：

10.1002/mana.201200315

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish a Trudinger-Moser type inequality in a weighted Sobolev space. The inequality is applied in the study of the elliptic equation -div(K(x)del u) = K(x) f (u) + h in R-2, where K(x) = exp(|x|(2)/4), f has exponential critical growth and h belongs to the dual of an appropriate function space. We prove that the problem has at least two weak solutions provided h not equal 0 is small. (C) 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：1255 / 1273

页数：19

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