| Summary: | We establish results on existence, non-existence, and asymptotic behavior of ground state solutions for the singular nonlinear elliptic problem $$displaylines{ -Delta u = g(u)| abla u |^2 + lambdapsi(x) f(u) quadhbox{in } mathbb{R}^N,\ u > 0 quadhbox{in } mathbb{R}^N,quad lim_{|x| o infty} u(x)=0, }$$ where $lambda in mathbb{R}$ is a parameter, $psi geq 0 $, not identically zero, is a locally Holder continuous function; $g:(0,infty) o mathbb{R}$ and $f:(0,infty) o (0,infty)$ are continuous functions, (possibly) singular in $0$; that is, $f(s)o infty$ and either $g(s)o infty$ or $g(s)o -infty$ as $s o 0$. The main purpose of this article is to complement the main theorem in Porru and Vitolo [15], for the case $Omega=mathbb{R}^N$. No monotonicity condition is imposed on f or g.
|
|---|