Fractional Kirchhoff-type equation with Hardy-Littlewood-Sobolev critical exponent

摘要

In this paper, we consider the following fractional Kirchhoff-type equation:(a + b integral(RN) integral(RN) vertical bar u(x) - u(y)vertical bar(2)/vertical bar x - y vertical bar(N+2s) dxdy) (-Delta)(s)u = (I-alpha * vertical bar u vertical bar(2h,alpha)*) vertical bar u vertical bar(2)(h,alpha)*(-2)u, in R-N,where N >= 3, s is an element of (0, 1), a > 0, b >= 0, alpha is an element of (0, N) and 2(h,alpha)* = N+alpha/N-2s is the Hardy-Littlewood-Sobolev critical exponent, and I, is the Riesz potential. We establish the existence, nonexistence and multiplicity of nontrivial solutions to above equation. (C) 2019 Published by Elsevier Ltd.