Existence of positive solutions of elliptic equations with Hardy term

Abstract

This paper is devoted to studying the existence of positive solutions of the problem: ( ∗ ) { − Δ u = u p | x | a + h ( x , u , ∇ u ) , in Ω , u = 0 , on ∂ Ω , where Ω ⊂ R N ( N ≥ 3 ) is an open bounded smooth domain with boundary ∂ Ω , and 1 < p < N − a N − 2 , 0 < a < 2 . Under suitable conditions of h ( x , u , ∇ u ) , we get a priori estimates for the positive solutions of problem ( ∗ ) . By making use of these estimates and topological degree theory, we further obtain some existence results for the positive solutions of problem ( ∗ ) when 1 < p < N − a N − 2 .