Existence of solutions for a coupled Schrödinger equations with critical exponent

Xiaoyong Qian; Jun Wang; Maochun Zhu; Xiaoyong Qian; Jun Wang; Maochun Zhu

doi:10.3934/era.2022140

Electronic Research Archive

2022, Volume 30, Issue 7: 2730-2747. doi: 10.3934/era.2022140

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Research article

Existence of solutions for a coupled Schrödinger equations with critical exponent

1.
School of Mathematical of Sciences, Jiangsu University, Zhenjiang, Jiangsu, 212013, China
2.
Institute of Applied System Analysis, Jiangsu University, Zhenjiang, Jiangsu, 212013, China

Received: 15 September 2021 Revised: 06 March 2022 Accepted: 06 March 2022 Published: 23 May 2022

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.
- coupled Schrödinger equations,
- Sobolev critical exponent,
- variational method,
- Nehari Manifold
Citation: Xiaoyong Qian, Jun Wang, Maochun Zhu. Existence of solutions for a coupled Schrödinger equations with critical exponent[J]. Electronic Research Archive, 2022, 30(7): 2730-2747. doi: 10.3934/era.2022140

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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.

References

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