LEAST ENERGY SIGN-CHANGING SOLUTIONS FOR THE NONLINEAR SCHRODINGER-POISSON SYSTEM

This article concerns the existence of the least energy sign-changing solutions for the Schrodinger-Poisson system -Delta u + V(x)u + lambda phi(x)u = f(u), in R-3, -Delta phi = u(2), in R-3. Because the so-called nonlocal term lambda phi(x) u is involved in the system, the variational functional of the above system has totally different properties from the case of lambda = 0. By constraint variational method and quantitative deformation lemma, we prove that the above problem has one least energy sign-changing solution. Moreover, for any lambda > 0, we show that the energy of a sign-changing solution is strictly larger than twice of the ground state energy. Finally, we consider lambda as a parameter and study the convergence property of the least energy sign-changing solutions as lambda SE arrow 0.