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 − Δ u = p ( x ) ( g ( u ) + f ( u ) + | ∇ u | a ) in R 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.