ISSN:
1432-0835
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. We investigate the existence of ground state solutions to the Dirichlet problem $-\div(|x|^\alpha\nabla u)=|u|^{2^*_\alpha-2}u$ in $\Omega$ , u = 0 on $\partial\Omega$ , where $\alpha\in(0,2)$ , $2^*_\alpha={2n\over n-2+\alpha}$ and $\Omega$ is a domain in ${\bf R}^n$ . In particular we prove that a non negative ground state solution exists when the domain $\Omega$ is a cone, including the case $\Omega={\bf R}^n$ . Moroever, we study the case of arbitrary domains, showing how the geometry of the domain near the origin and at infinity affects the existence or non existence of ground state solutions.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s005260050130
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