Multiple and least energy sign-changing solutions for Schrodinger-Poisson equations in R3 with restraint

Abstract

In this paper, we study the existence of multiple sign-changing solutions with a prescribed Lp+1−norm and the
existence of least energy sign-changing restrained solutions for the following nonlinear Schr¨odinger-Poisson system:

By choosing a proper functional restricted on some appropriate subset to using a method of invariant sets of descending flow,
we prove that this system has infinitely many sign-changing solutions with the prescribed Lp+1−norm and has a least energy for
such sign-changing restrained solution for p ∈ (3, 5). Few existence results of multiple sign-changing restrained solutions are
available in the literature. Our work generalize some results in literature.