Ground states for a coupled Schrödinger system with general nonlinearities

We study a coupled Schrödinger system with general nonlinearities. By using variational methods, we prove the existence and asymptotic behaviour of ground state solution for the system with periodic couplings. Moreover, we prove the existence and nonexistence of ground state solution for the system...

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Veröffentlicht in:	Boundary value problems 2020-01, Vol.2020 (1), p.1-24, Article 22
Hauptverfasser:	Duan, Xueliang, Wei, Gongming, Yang, Haitao
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Approximations and Expansions Asymptotic methods Asymptotic properties Coupled Schrödinger system Couplings Difference and Functional Equations Ground state Ground state solutions Mathematics Mathematics and Statistics Nehari manifold Ordinary Differential Equations Partial Differential Equations Variational methods
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Beschreibung
Zusammenfassung:	We study a coupled Schrödinger system with general nonlinearities. By using variational methods, we prove the existence and asymptotic behaviour of ground state solution for the system with periodic couplings. Moreover, we prove the existence and nonexistence of ground state solution for the system with non-periodic couplings via Nehari manifold method. Especially, the ground state solution with both nontrivial components is obtained, and the sign of nontrivial components is considered.
ISSN:	1687-2770 1687-2762 1687-2770
DOI:	10.1186/s13661-020-01331-6