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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 (catrinaf@stjohns.edu)
Marcelo Furtado
Affiliation:
Departamento de Matemática, Universidade de Brasília, CEP 70910-900, Brasília, DF, Brazil (mfurtado@unb.br)
Marcelo Montenegro
Affiliation:
Departamento de Matemática, Universidade Estadual de Campinas, IMECC, Caixa Postal 6065, CEP 13083-970, Campinas, SP, Brazil (msm@ime.unicamp.br)
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Abstract

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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