Geodesic
Existence and multiplicity of normalized solutions for a class of fractional Schrödinger–Poisson equations
Zhipeng Yang1 ; Fukun Zhao1 ; Shunneng Zhao2
1Yunnan Normal University, Department of Mathematics
2Yunnan 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 
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
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     title = {Existence and multiplicity of normalized solutions for a class of fractional {Schr\"odinger{\textendash}Poisson} equations},
     journal = {Annales Fennici Mathematici},
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     doi = {10.54330/afm.119450},
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