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

作　　者：Nemat NYAMORADI Abdolrahman RAZANI 

机构地区：[1]Department of Mathematics,Razi University,Kermanshah,Iran [2]Department of Pure Mathematics,Faculty of Science,Imam Khomeini International University,34149-16818,Qazvin,Iran

出　　处：《Acta Mathematica Scientia》2021年第4期1321-1332,共12页数学物理学报（B辑英文版）

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 0<s<1<p,0<μ<N,N>ps,a,b>0,λ>0 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 inequality.We get the existence of infinitely many solutions for the above problem by using the concentration compactness principle and Krasnoselskii’s genus theory.To the best of our knowledge,our result is new even in Choquard-Kirchhoff-type equations involving the p-Laplacian case.

关 键 词：Hardy-Littlewood-Sobolev inequality concentration-compactness principle variational method Fractional p-Laplacian operators multiple solutions 

分 类 号：O175[理学—数学]