Multiple solutions for nonhomogeneous Schrodinger-Kirchhoff type equations involving the fractional p-Laplacian in RN

In this paper we investigate the existence of multiple solutions for the nonhomogeneous fractional p-Laplacian equations of Schrodinger-Kirchhoff type M(integral integral(R2N) vertical bar u(x) - u(y)vertical bar(p)/vertical bar x - y vertical bar(N+ps) dxdy) (-Delta)(p)(s) u + V(x)vertical bar u vertical bar(p-2)u = f (x, u) + g(x) in RN, where (-Delta)(p)(s) is the fractional p-Laplacian operator, with 0 < s < 1 < p < infinity and ps < N, the nonlinearity f : R-N x R (R): R is a Caratheodory function and satisfies the Ambrosetti-Rabinowitz condition, V : R-N (R) R+ is a potential function and g : R-N (R) R is a perturbation term. We first establish Batsch-Wang type compact embedding theorem for the fractional Sobolev spaces. Then multiplicity results are obtained by using the Ekeland variational principle and the Mountain Pass theorem.