Positive Solutions and Infinitely Many Solutions for a Weakly Coupled System

Positive Solutions and Infinitely Many Solutions for a Weakly Coupled System

We study a Schrödinger system with the sum of linear and nonlinear couplings. Applying index theory, we obtain infinitely many solutions for the system with periodic potentials. Moreover, by using the concentration compactness method, we prove the existence and nonexistence of ground state solutions...

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Veröffentlicht in:Acta mathematica scientia 2020-09, Vol.40 (5), p.1585-1601
Hauptverfasser: Duan, Xueliang, Wei, Gongming, Yang, Haitao
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Mathematics
Mathematics and Statistics
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Beschreibung
Zusammenfassung:We study a Schrödinger system with the sum of linear and nonlinear couplings. Applying index theory, we obtain infinitely many solutions for the system with periodic potentials. Moreover, by using the concentration compactness method, we prove the existence and nonexistence of ground state solutions for the system with close-to-periodic potentials.
ISSN:0252-9602
1572-9087
DOI:10.1007/s10473-020-0523-9