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Research Article | Open Access

Existence of solutions for a coupled Schrödinger equations with critical exponent

Xiaoyong Qian1, Jun Wang2( ), Maochun Zhu1
School of Mathematical of Sciences, Jiangsu University, Zhenjiang, Jiangsu, 212013, China
Institute of Applied System Analysis, Jiangsu University, Zhenjiang, Jiangsu, 212013, China
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Abstract

In this paper we study the existence of multiple nontrivial solutions of the coupled Schrödinger system with external sources terms as perturbations. This type of the system arises from Bose-Einstein condensate. As these external sources terms are nonlinear functions and small in some sense, we use fibre map to divide the Nehari manifold into threes parts, and then prove the existence of a nontrivial ground state solution and a bound state solution.

Keywords

coupled Schrödinger equationsSobolev critical exponentvariational methodNehari Manifold

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Electronic Research Archive
Volume 30 Issue 7,
July 2022
Pages 2730-2747
DOI: 10.3934/era.2022140

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Cite this article:
Qian X, Wang J, Zhu M. Existence of solutions for a coupled Schrödinger equations with critical exponent. Electronic Research Archive, 2022, 30(7): 2730-2747. https://doi.org/10.3934/era.2022140

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Received: 15 September 2021
Revised: 06 March 2022
Accepted: 06 March 2022
Published: 15 July 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)