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Infinitely Many Sign-Changing Solutions for the Nonlinear Schrödinger-Poisson System with Super 2-linear Growth at Infinity

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Abstract

In this paper, we investigate the sign-changing solutions to the following Schrödinger-Poisson system

$$\begin{aligned} \qquad \left\{ \begin{array}{ll} -\Delta u+V(x)u+\lambda \phi (x) u =f(u),\ \ \ &{}\ x \in {\mathbb {R}}^{3},\\ -\Delta \phi =u^2, \ \ \ &{}\ x \in {\mathbb {R}}^{3}, \\ \end{array} \right. \end{aligned}$$

where \(\lambda >0\) is a parameter and f is super 2-linear at infinity. By using the method of invariant sets of descending flow and a multiple critical points theorem, we prove that this system possesses infinitely many sign-changing solutions for any \(\lambda >0\).

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  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China

    Shuai Wang, Xing-Ping Wu & Chun-Lei Tang

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Wang, S., Wu, XP. & Tang, CL. Infinitely Many Sign-Changing Solutions for the Nonlinear Schrödinger-Poisson System with Super 2-linear Growth at Infinity. Qual. Theory Dyn. Syst. 22, 56 (2023). https://doi.org/10.1007/s12346-023-00757-4

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