Ground state solution of Fractional Schrödinger-Poisson-Slater equation: Double critical case

Yu Su; Zhaosheng Feng

doi:10.3934/dcdss.2024206

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2024. Doi: 10.3934/dcdss.2024206

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Ground state solution of Fractional Schrödinger-Poisson-Slater equation: Double critical case

Yu Su^1, and
Zhaosheng Feng^2, ,

1.
School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, Anhui 232001, China
2.
School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, Texas 78539, USA

^*Corresponding author: Zhaosheng Feng
^*Corresponding author: Zhaosheng Feng

Received: August 2024

Early access: November 2024

The first author is supported by Natural Science Research Project of Anhui Educational Committee (Grant No. 2023AH040155).

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Abstract

The fractional Schrödinger-Poisson-Slater equation can be derived from the Thomas-Fermi-Dirac-von Weizsäcker theory of charge screening in graphene. In this paper, we make an effort to study the behavior of bounded sequences in radial fractional Coulomb-Sobolev space under certain conditions, and then apply it to study the existence of Nehari-Pohožaev type ground state solutions for the fractional Schrödinger-Poisson-Slater equation with lower and upper critical exponents.

Keywords:

Fractional Schrödinger-Poisson-Slater equation,
critical exponent,
Nehari-Pohožaev manifold,
ground state,
fractional Coulomb-Sobolev space.

Mathematics Subject Classification: Primary: 35J60; Secondary: 35J20.

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