Multiple solutions for a coupled Kirchhoff system with fractional p-Laplacian and sign-changing weight functions

摘要

In this paper, we investigate the multiplicity of solutions for Kirchhoff fractional p-Laplacian system in bounded domains: @@@ {(Sigma(k)(i=1)[u(i)](s,p)(p))(theta-1) (-Delta)(p)(s)u(j)(x) @@@ =lambda(j)f(j)(x)vertical bar u(j)vertical bar(q-2)u(j)+Sigma(i not equal j)beta(i,)jh(x)vertical bar u(j)vertical bar(m-2)u(j) in Omega, @@@ u(j)=0 in R-n \Omega. @@@ By using the Nehari manifold method, together with Ekeland's variational principle, we show that there exist two distinct solutions under suitable conditions on weight functions f(j) and h. Our results extend and generalize the main results in Xiang et al. [Multiplicity of solutions for a class of quasilinear Kirchhoff system involving the fractional p-Laplacian. Nonlinearity. 2016;29:3186-3205] in Nonlinearity 2016, in which f(j), h are constants.

关键词