Existence and multiplicity of normalized solutions for a class of fractional Schrödinger–Poisson equations

Authors

  • Zhipeng Yang Yunnan Normal University, Department of Mathematics
  • Fukun Zhao Yunnan Normal University, Department of Mathematics
  • Shunneng Zhao Yunnan Normal University, Department of Mathematics, and Zhejiang Normal University, Department of Mathematics

Keywords:

Variational method, fractional Schrödinger-Poisson, normalized solutions

Abstract

 

We consider the fractional Schrödinger-Poisson equation
\(\begin{cases}(-\Delta)^su-\lambda u+\phi u=|u|^{p-2}u,& x\in\mathbb{R}^3,\\ (-\Delta)^t\phi=u^2,& x\in\mathbb{R}^3,\end{cases}\)
where \(s,t\in(0,1)\) satisfies \(2s+2t>3\), \(p\in(\frac{4s+6}{3},2^*_s)\) and \(\lambda\in\mathbb{R}\) is an undetermined parameter. We deal with the case where the associated functional is not bounded below on the \(L^2\)-unit sphere and show the existence of infinitely many solutions \((u,\lambda)\) with \(u\) having prescribed \(L^2\)-norm.
Section
Articles

Published

2022-05-18

How to Cite

Yang, Z., Zhao, F., & Zhao, S. (2022). Existence and multiplicity of normalized solutions for a class of fractional Schrödinger–Poisson equations. Annales Fennici Mathematici, 47(2), 777–790. https://doi.org/10.54330/afm.119450