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
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页码：1255 / 1273
页数：19
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