POSITIVE SOLUTIONS FOR KIRCHHOFF-SCHRODINGER-POISSON SYSTEMS WITH GENERAL NONLINEARITY

In the present paper the following Kirchhoff-Schriidinger-Poisson system is studied: {-(a+b integral(R3) vertical bar del u vertical bar(2) dx) Delta u + mu phi(x)u =f(u) in R-3, {-Delta phi = mu u(2) in R-3, where a > 0, b >= 0 are constants and mu > 0 is a parameter, f is an element of C([8, R). Without assuming the Ambrosetti-Rabinowitz type condition and monotonicity condition on f, we establish the existence of positive radial solutions for the above system by using variational methods combining a monotonicity approach with a delicate cut-off technique. We also study the asymptotic behavior of solutions with respect to the parameter mu. In addition, we obtain the existence of multiple solutions for the nonhomogeneous case corresponding to the above problem. Our results improve and generalize some known results in the literature.