Geodesic
Existence and multiplicity of normalized solutions for a class of fractional Schrödinger–Poisson equations
Zhipeng Yang1 ; Fukun Zhao1 ; Shunneng Zhao2
1 Yunnan Normal University, Department of Mathematics
2 Yunnan Normal University, Department of Mathematics, and Zhejiang Normal University, Department of Mathematics
Annales Fennici Mathematici, Tome 47 (2022) no. 2, pp. 777-790.

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  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 $s,t\in(0,1)$ satisfy $2s+2t>3$, $p\in(\frac{4s+6}{3},2^*_s)$ 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.
DOI : 10.54330/afm.119450
Keywords: Variational method, fractional Schrödinger-Poisson, normalized solutions

Zhipeng Yang 1 ; Fukun Zhao 1 ; Shunneng Zhao 2

1 Yunnan Normal University, Department of Mathematics
2 Yunnan Normal University, Department of Mathematics, and Zhejiang Normal University, Department of Mathematics 
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Zhipeng Yang; Fukun Zhao; Shunneng Zhao. Existence and multiplicity of normalized solutions for a class of fractional Schrödinger–Poisson equations. Annales Fennici Mathematici, Tome 47 (2022) no. 2, pp. 777-790. doi : 10.54330/afm.119450. http://geodesic.mathdoc.fr/articles/10.54330/afm.119450/

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