Ground state solutions for the singular Lane-Emden-Fowler equation with sublinear convection term

Marius Ghergu (1) , Vicentiu Radulescu (1)

1 UCV - Department of Mathematics

We are concerned with singular elliptic equations of the form $-\Delta u= p(x)(g(u)+ f(u)+|\nabla u|^a)$ in $\RR^N$ ($N\geq 3$), where $p$ is a positive weight and $0< a <1$. Under the hypothesis that $f$ is a nondecreasing function with sublinear growth and $g$ is decreasing and unbounded around the origin, we establish the existence of a ground state solution vanishing at infinity. Our arguments rely essentially on the maximum principle.

Mots clés: ground state solution; singular elliptic equation; convection term; maximum principle

Domaines: Equations aux dérivées partielles [math.AP]

Marius Ghergu, Vicentiu Radulescu. Ground state solutions for the singular Lane-Emden-Fowler equation with sublinear convection term. 2006. ⟨hal-00106183⟩