EXISTENCE OF INFINITELY MANY SMALL SOLUTIONS FOR SUBLINEAR FRACTIONAL KIRCHHOFF-SCHRODINGER-POISSON SYSTEMS

We study the Kirchhoff-Schrodinger-Poisson system m([u](alpha)(2))(-Delta)(alpha )u + V(x)u + k(x)phi u = f(x, u), x is an element of R-3, (-Delta)(beta)phi = k(x)u(2), x is an element of R-3, where [.](alpha) denotes the Gagliardo semi-norm, (-Delta)(alpha) denotes the fractional Laplacian operator with alpha, beta is an element of (0, 1], 4 alpha +2 beta >= 3 and m : [0, +infinity) -> [0, +infinity) is a Kirchhoff function satisfying suitable assumptions. The functions V(x) and k(x) are nonnegative and the nonlinear term f (x, s) satisfies certain local conditions. By using a variational approach, we use a Kajikiya's version of the symmetric mountain pass lemma and Moser iteration method to prove the existence of infinitely many small solutions.