LEAST ENERGY SIGN-CHANGING SOLUTIONS FOR SUPER-QUADRATIC SCHRÖDINGER-POISSON SYSTEMS IN <inline-formula><tex-math id="M1">$ \mathbb{R}^{3} $</tex-math></inline-formula>

Abstract

<abstract> In this paper, we study the following Schrödinger-Poisson systems <p class="disp_formula">$ \begin{equation*} \begin{cases} -\Delta u+Vu+\lambda \phi u = f(u), &amp;\quad x \in \mathbb{R}^{3},\\ -\Delta \phi = u^{2}, &amp;\quad x \in \mathbb{R}^{3}, \end{cases} \end{equation*} $ where $ V, \: \lambda&gt;0 $ and $ f \in C\left(\mathbb{R}, \mathbb{R}\right) $. Under some relaxed assumptions on $ f $, using variational methods in combination with the Pohozǎev identity, we prove that the above system possesses a least energy sign-changing solution and a ground state solution provided that $ \lambda $ is sufficiently small. Moreover, we prove that the energy of a sign-changing solution is strictly larger than that of the ground state solution. Our results generalize and extend some recent results in the literature. </abstract>