A remark on ground state solutions for Lane-Emden-Fowler equations with a convection term

Abstract

Via a sub-supersolution method and a perturbation argument, we study the Lane-Emden-Fowler equation -Δu = p(x) [g(u) + ƒ(u) + |∇u|q] in ℝN (N ≥ 3), where 0 < q < 1, p is a positive weight such that ∫∞0 rφ(r)dr < ƒ are sublinear, which include no monotonicity on the functions g(u), ƒ(u), g(u)/u and ƒ(u)/u, we show the existence of ground state solutions.