A GENERALIZED CHOQUARD EQUATION WITH WEIGHTED ANISOTROPIC STEIN-WEISS POTENTIAL ON A NONREFLEXIVE ORLICZ-SOBOLEV SPACES  

作　　者：Lucas DA SILVA Marco A.S.SOUTO 

机构地区：[1]Unidade Academica de Matematica,Federal University of Campina Grande,Campina Gran Paraiba 58429-970,Brazil

出　　处：《Acta Mathematica Scientia》2025年第2期569-601,共33页数学物理学报(B辑英文版)

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).

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.

关 键 词：Orlicz-Sobolev spaces variational methods Choquard equation nonrefexive spaces 

分 类 号：O175.25[理学—数学]