Multiplicity of solutions for a class of quasilinear Kirchhoff system involving the fractionalp-Laplacian

In this paper, we investigate the multiplicity of solutions for a p-Kirchhoff system driven by a nonlocal integro-differential operator with zero Dirichlet boundary data. As a special case, we consider the following fractional p-Kirchhoff system {(∑i=1k[ui]s,pp)θ−1(−Δ)psuj(x)=λj|uj|q−2uj+∑i≠jβij|ui|m|uj|m−2ujin Ω,uj=0in RN\Ω, where , , , , is an open bounded subset of with Lipschitz boundary , N > ps with , is the fractional p-Laplacian, and for , . When and for all , two distinct solutions are obtained by using the Nehari manifold method. When and for all or and for all , the existence of infinitely many solutions is obtained by applying the symmetric mountain pass theorem. To our best knowledge, our results for the above system are new in the study of Kirchhoff problems.