NON-AUTONOMOUS SCHRODINGER-POISSON SYSTEM IN R3

We study the existence of positive solutions for the non-autonomous Schrodinger-Poisson system: { -Delta u + u + lambda K (x) phi u = a (x) vertical bar u vertical bar(p-2) u in R-3, -Delta phi = K (x) u(2) in R-3, where lambda > 0, 2 < p <= 4 and both K (x) and a (x) are nonnegative functions in R-3, which satisfy the given conditions, but not require any symmetry property. Assuming that lim(vertical bar x vertical bar ->infinity) K (x) = K-infinity >= 0 and lim(vertical bar x vertical bar ->infinity) a (x) = a(infinity) > 0, we explore the existence of positive solutions, depending on the parameters lambda and p. More importantly, we establish the existence of ground state solutions in the case of 3.18 approximate to 1+root 73/3 < p <= 4.