Ground state solutions and decay estimation of Choquard equation with critical exponent and Dipole potential

Yu Su; Zhaosheng Feng

doi:10.3934/dcdss.2022112

Article Contents

2023, Volume 16, Issue 3&4: 589-601. Doi: 10.3934/dcdss.2022112

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Ground state solutions and decay estimation of Choquard equation with critical exponent and Dipole potential

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

Received: February 2022

Revised: April 2022

Early access: May 2022

Published: March 2023

This work is supported by the Key Program of University Natural Science Research Grant of Anhui Province (KJ2020A0292)

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Abstract

In this paper, we study a class of Choquard equations with critical exponent and Dipole potential. We prove the existence of radial ground state solutions for Choquard equations by using the refined Sobolev inequality with the Morrey norm, and show that any nonnegative weak solutions of Choquard equations have additional decay properties in terms of ground state representation.

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Mathematics Subject Classification: 35Q40, 35J50.

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References

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