Existence of multiple solutions for nonhomogeneous Schroedinger-Kirchhoff system involving the fractional p-Laplacian with sign-changing potential

摘要

In this paper, we prove the existence of multiple solutions for the following Schrodinger-Kirchhoff system involving the fractional p-Laplacian{M(integral integral R-2n 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-u(x, u, v) + lambda g(x), x epsilon R-N,M(integral integral R-2n vertical bar v(x)-v(y)vertical bar(p)/vertical bar x-y vertical bar(N+ps) dxdy) (-Delta)(p)(s)u+V(x)vertical bar v vertical bar(p-2)v = Fv(x, u, v) + lambda h(x), x epsilon R-N,u(x) - 0, v(x) - 0, as vertical bar x vertical bar where (-Delta)(p)(s) denotes the fractional p-Laplacian of order s epsilon (0, 1), 2 = p infinity, ps N, F-u = partial derivative F/partial derivative u, F-v = partial derivative F/partial derivative v V(x) is allowed to be sign-changing, lambda 0 and g, h : R-N - R is a perturbation. Under some certain assumptions on f, we obtain the existence of multiple solutions for this problem via Ekeland's variational principle and mountain pass theorem. (C) 2019 Elsevier Ltd. All rights reserved. - +infinity,