Ground state, bound states and bifurcation properties for a Schrodinger-Poisson system with critical exponent

Abstract

This article concerns the existence of ground state and bound states, and the study of their bifurcation properties for the Schrödinger-Poisson system -Δu + u + φu = |u|4u + µh(x)u, -Δφ = u2 in ℝ3. Under suitable assumptions on the coefficient h(x), we prove that the ground state must bifurcate from zero, and that another bound state bifurcates from a solution, when µ = µ1 is the first eigenvalue of -Δu + u = µh(x)u in H1(ℝ3).