Ground state solutions for the singular Lane-Emden-Fowler equation with sublinear convection term
Abstract
We are concerned with singular elliptic equations of the form
−Δu=p(x)(g(u)+f(u)+|∇u
|
a
)
in $\RR^N$ (
N≥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.