EXISTENCE TO FRACTIONAL CRITICAL EQUATION WITH HARDY-LITTLEWOOD-SOBOLEV NONLINEARITIES

作     者：Nemat NYAMORADI Abdolrahman RAZANI Nemat NYAMORADI;Abdolrahman RAZANI

作者机构：Department of MathematicsRazi UniversityKermanshahIran Department of Pure MathematicsFaculty of ScienceImam Khomeini International University34149-16818QazvinIran 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2021年第41卷第4期

页      面：1321-1332页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：Hardy-Littlewood-Sobolev inequality concentration-compactness principle variational method Fractional p-Laplacian operators multiple solutions 

摘      要：In this paper,we consider the following new Kirchhoff-type equations involving the fractional p-Laplacian and Hardy-Littlewood-Sobolev critical nonlinearity:(A+B∫∫_(R^(2N))|u(x)-u(y)|^(p)/|x-y|^(N+ps)dxdy)^(p-1)(-△)_(p)^(s)u+λV(x)|u|^(p-2)u=(∫_(R^(N))|U|^(P_(μ,S)^(*))/|x-y|^(μ)dy)|u|^(P_(μ,S)^(*))^(-2)u,x∈R^(N),where(-△)_(p)^(s)is the fractional p-Laplacian with 00,λ0 is a parameter,V:R^(N)→R^(+)is a potential function,θ∈[1,2_(μ,s)^(*))and P_(μ,S)^(*)=pN-pμ/2/N-ps is the critical exponent in the sense of Hardy-Littlewood-Sobolev *** get the existence of infinitely many solutions for the above problem by using the concentration compactness principle and Krasnoselskii’s genus *** the best of our knowledge,our result is new even in Choquard-Kirchhoff-type equations involving the p-Laplacian case.