EXISTENCE AND CONCENTRATION OF POSITIVE SOLUTIONS FOR SCHRODINGER-POISSON SYSTEMS WITH STEEP WELL POTENTIAL

This paper is devoted to study the following Schrodinger-Poisson system { -Delta u + (lambda a(x) + b(x))u + K(x)phi u = f (u), x is an element of R-3, -Delta phi = 4 pi K(x)u(2), x is an element of R-3, where lambda is a positive parameter, a is an element of C (R-3, R-broken vertical bar) has a bounded potential well Omega = a (1)(0), b is an element of C(R-3, R) is allowed to be sign-changing, K is an element of C (R-3, R+) and f is an element of C(R, R). Without the monotonicity of f(t) / vertical bar t vertical bar(3) and the Ambrosetti-Rabinowitz type condition, we establish the existence and exponential decay of positive multi-bump solutions of the above system for lambda >= (Lambda) over bar, and obtain the concentration of a family of solutions as lambda -> +infinity, where (Lambda) over bar > 0 is determined by terms of a, b, K and f. Our results improve and generalize the ones obtained by C. O. Alves, M. B. Yang [3] and X. Zhang, S. W. Ma [38].