Semiclassical ground state solutions for critical Schrodinger-Poisson systems with lower perturbations

In this paper, we study the following singularly perturbed Schrodinger-Poisson system {-epsilon(2) Delta u + V(x)u + phi u = f(u) + u(5), x is an element of R-3, -epsilon(2)Delta phi = u(2), x is an element of R-3, where epsilon is a small positive parameter, V is an element of C(R-3, R) and f is an element of C(R, R) satisfies neither the usual Ambrosetti-Rabinowitz type condition nor any monotonicity condition on f (u)/u(3). By using some new techniques and subtle analysis, we prove that there exists a constant epsilon(0) > 0 determined by V and f such that for epsilon is an element of (0, epsilon(0)] the above system admits a semiclassical ground state solution (v) over cap (epsilon) with exponential decay at infinity. We also study the asymptotic behavior of {(v) over cap (epsilon}) as epsilon -> 0. In particular, our results can be applied to the nonlinearity f(u) similar to vertical bar u vertical bar(q-2)u for q is an element of [3, 4], and extend the previous work that only deals with the case in which f(u) similar to vertical bar u vertical bar(q-2)u for q is an element of (4, 6)268626722716National Natural Science Foundation of ChinaNational Natural Science Foundation of China [11971485