Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-12-01T01:53:35.627Z Has data issue: false hasContentIssue false
  • English
  • Français

Positive solutions for nonlinear elliptic equations with fast increasing weights

Published online by Cambridge University Press:  03 December 2007

Florin Catrina ,
Marcelo Furtado  and
Marcelo Montenegro
Florin Catrina
Affiliation:
Department of Mathematics and Computer Science, St. John's University, Queens, NY 11439, USA ([email protected])
Marcelo Furtado
Affiliation:
Departamento de Matemática, Universidade de Brasília, CEP 70910-900, Brasília, DF, Brazil ([email protected])
Marcelo Montenegro
Affiliation:
Departamento de Matemática, Universidade Estadual de Campinas, IMECC, Caixa Postal 6065, CEP 13083-970, Campinas, SP, Brazil ([email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

We find positive rapidly decaying solutions for the equation

$$ -\text{div}(K(x)\nabla u)=K(x)u^{2^*-1}+\lambda K(x)|x|^{\alpha-2}u $$

in $\mathbb{R}^N$, where $N\geq3$, the nonlinearity is given by the critical Sobolev exponent $2^*=2N/(N-2)$, the weight is $K(x)=\exp(\tfrac14|x|^\alpha)$, $\alpha\geq2$ and $\lambda$ is a parameter.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 137 , Issue 6 , December 2007 , pp. 1157 - 1178
Copyright
2007 Royal Society of Edinburgh

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)