Electron. J. Differential Equations, Vol. 2019 (2019), No. 127, pp. 1-18.

Existence, characterization and number of ground states for coupled equations

Qihan He, Shuangjie Peng

This article concerns the existence, characterization and number of ground states for the system consisting of m coupled semilinear equations

We extend the characterization results obtained by Correia [5,6] to the above problem. Also we give a new characterization of the ground states, which provides a more convenient way for finding or checking ground states. This study may be the first result not only positive ground states but also for semi-trivial ground states, and it shows that the positive ground state is unique for some special cases.

Submitted July 18, 2018. Published November 26, 2019.
Math Subject Classifications: 35B99, 35J47, 35J60.
Key Words: Coupled equations; ground states.

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Qihan He
College of Mathematics and Information Science
Guangxi University
Nanning 530003, China
email: heqihan277@163.com
Shuangjie Peng
School of Mathematics and Statistics
Central China Normal University
Wuhan 430079, China
email: sjpeng@mail.ccnu.edu.cn

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