MULTIPLE POSITIVE SOLUTIONS FOR SCHRODINGER-POISSON SYSTEM IN R3 INVOLVING CONCAVE-CONVEX NONLINEARITIES WITH CRITICAL EXPONENT

In this paper, we study the existence of multiple positive solutions of the following Schrodinger-Poisson system with critical exponent { -Delta u - l(x)phi u = lambda h(x)vertical bar u vertical bar(q-2)u + vertical bar u vertical bar(4)u, in R-3, -Delta phi = l(x)u(2), in R-3, where 1 < q < 2 and lambda > 0. Under some appropriate conditions on l and h, we show that there exists lambda* > 0 such that the above problem has at least two positive solutions for each lambda is an element of (0, lambda*) by using the Mountain Pass Theorem and Ekeland's Variational Principle.