Infinitely many solutions for a fractional Kirchhoff type problem via Fountain Theorem

In this paper, we use the Fountain Theorem and the Dual Fountain Theorem to study the existence of infinitely many solutions for Kirchhoff type equations involving nonlocal integro-differential operators with homogeneous Dirichlet boundary conditions. A model for these operators is given by the fractional Laplacian of Kirchhoff type: {M(integral integral(R2N) vertical bar u(x) - u(y)vertical bar(2)/vertical bar x - y vertical bar(N+2s) dxdy) (-Delta)(s) u(x) - lambda u = f(x, u) in Omega u = 0 in R-N\Omega, where Omega is a smooth bounded domain of R-N, (-Delta)(s) is the fractional Laplacian operator with 0 < s < 1 and 2s < N, lambda is a real parameter, M is a continuous and positive function and f is a Caratheodory function satisfying the Ambrosetti-Rabinowitz type condition. (C) 2015 Elsevier Ltd. All rights reserved.