THREE POSITIVE SOLUTIONS FOR THE INDEFINITE FRACTIONAL SCHRODINGER-POISSON SYSTEMS

In this paper, we are concerned with the following fractional Schrodinger-Poisson systems with concave-convex nonlinearities: (-Delta(s)u + u + mu l(x)phi u = f(x)vertical bar u vertical bar(p) (2)u + g (x)vertical bar u vertical bar(q-2)u in R-3, (-Delta)(t)phi = l(x)u(2) in R-3 , where 1/2 < t <= s < 1, 1 < q < 2 < p < min{4, 2(s)*}, 2(s)* = 6/(3 - 2s), and mu > 0 is a parameter, f is an element of C(R-3) is sign-changing in R-3 and g is an element of Lp/(p-q) (R-3). Under some suitable assumptions on l(x), f (x) and g(x), we explore that the energy functional corresponding to the system is coercive and bounded below on H-alpha (R-3) which gets a positive solution. Furthermore, we constructed some new estimation techniques, and obtained other two positive solutions. Recent results from the literature are generally improved and extended.