A NOTE ON SIGN-CHANGING SOLUTIONS FOR THE SCHRODINGER POISSON SYSTEM

We consider the following nonlinear Schrodinger-Poisson system {-Delta u + u + lambda phi(x)u = f(u) x is an element of R-3, -Delta phi = u(2), lim(vertical bar x vertical bar ->infinity) phi(x) = 0 x is an element of R-3, where lambda > 0 and f is continuous. By combining delicate analysis and the method of invariant subsets of descending flow, we prove the existence and asymptotic behavior of infinitely many radial sign-changing solutions for odd f. The nonlinearity covers the case of pure power-type nonlinearity f(u) = vertical bar u vertical bar p-2u with the less studied situation p is an element of (3,4). This result extends and complements the ones in [Z. Liu, Z. Q. Wang, and J. Zhang, Ann. Mat. Pura Appl., 2016] from the coercive potential case to the constant potential case.