Nonexistence of least energy nodal solutions for Schrödinger-Poisson equation

In this paper, we are interested in the least energy nodal solutions for nonlinear Schrödinger-Poisson equation in R3. Because the presence of the nonlocal term λϕu(x)u makes the variational functional of this equation totally different from the case of λ=0. It is still unknown whether the least energy nodal solution in H1(R3) exists or not when λ>0, although a sign-changing radial solution of this equation has been obtained in Wang and Zhou (2015). By introducing an odd Nehari manifold, we give a negative answer of this question when p∈(3,5) and λ>0, via the so-called “energy doubling” property.