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

We are concerned with singular elliptic equations of the form − u = p(x)(g(u)+f (u)+|∇u|a) in RN (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. © 2006 Elsevier Inc. All rights reserved