摘要
In this paper we investigate the existence of solution for the following nonlocal problem with Stein-Weiss convolution term-△Φu+V(x)Φ(|u|)u=1/|x|α(∫R^(N)K(y)F(u(y))/|x-y|Y(λ)|y|^(α)dy)K(x)f(u(x)),x∈R^(N),where a≥0,N≥2,λ>0 is a positive parameter,V,K∈C(R^(N),[0,∞))are nonne-gative functions that may vanish at infinity,the function f E C(R,R)is quasicritical and F(t)=∫_(0)^(t)f(s)ds.To establish our existence and regularity results,we use the Hardy-type inequalities for Orlicz-Sobolev Space and the Stein-Weiss inequality together with a varia-tional technique based on the mountain pass theorem for a functional that is not necessarily in C'.Furthermore,we also prove the existence of a ground state solution by the method of Nehari manifold in the case where the strict monotonicity condition on f is not required.This work incorporates the case where the N-functionΦdoes not verify the△_(2)-condition.
基金
supported by FAPESQ/Brazil(Grant No.3031/2021)
supported by CNPq/Brazil(Grant No.309.692/2020-2)and FAPESQ/Brazil(Grant No.3031/2021).
作者简介
Lucas DA SILVA,E-mail:ls3@academico.ufpb.br;Marco A.S.SOUTO,E-mail:marco@dme.ufcg.edu.br。
