Existence results for a nonlinear integral system of the Hardy–Hénon type in a bounded domain

Abstract

This paper investigates the existence and nonexistence of positive solutions for a weighted integral system associated with the weighted Hardy–Littlewood–Sobolev inequalities in a bounded domain Ω⊂Rn. We apply the mountain pass theorem to demonstrate the existence of a solution to this system and prove the nonexistence of a solution for it by means of the Pohozaev identity. We also use the above methods to prove the existence and nonexistence of positive solutions for a Hénon-type integral system.