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August, 2021 Solutions of Perturbed Fractional Schrödinger–Poisson System with Critical Nonlinearity in $\mathbb{R}^{3}$
Lvzhou Zheng
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Taiwanese J. Math. 25(4): 775-791 (August, 2021). DOI: 10.11650/tjm/201204

Abstract

In this paper, we study the existence of semiclassical solutions of the fractional Schrödinger–Poisson system with critical exponent in $\mathbb{R}^{3}$. Under suitable assumptions, we show that the problem has at least one nontrivial solution provided that $\epsilon \leq \varepsilon_{\delta}$ where $\varepsilon_{\delta}$ is sufficiently small positive number.

Funding Statement

The work was supported by the National Natural Science Foundation of China, No. 11601139, Hubei Provincial Natural Science Foundation of China, No. 2019CFB522 and Scientific Research and Innovation Team of Hubei Normal University, No. 2019CZ010.

Citation

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Lvzhou Zheng. "Solutions of Perturbed Fractional Schrödinger–Poisson System with Critical Nonlinearity in $\mathbb{R}^{3}$." Taiwanese J. Math. 25 (4) 775 - 791, August, 2021. https://doi.org/10.11650/tjm/201204

Information

Received: 20 August 2020; Revised: 4 December 2020; Accepted: 7 December 2020; Published: August, 2021
First available in Project Euclid: 15 December 2020

Digital Object Identifier: 10.11650/tjm/201204

Subjects:
Primary: 35B99 , 35J10 , 35J60

Keywords: Critical nonlinearity , fractional Schrödinger–Poisson system , variational methods

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

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Vol.25 • No. 4 • August, 2021
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