Existence results for a nonlinear integral system of the Hardy-Hénon type in a bounded domain (Q6542814)

This paper investigates the existence and nonexistence of positive solutions for a weighted nonlinear integral system in a star shaped with respect to the origin bounded domain \(\Omega\subset\mathbb{R}^n\). The problem about existence of a positive solution is transformed into the study of critical points of a functional associated with the weighted Hardy-Littlewood-Sobolev inequalities of the system. The mountain pass theorem is used. The nonexistence of a solution for the system is proved by means of the Pohozaev identity. Moreover the authors use the above methods to prove the existence and nonexistence of positive solutions for a Hénon-type integral system.