Subharmonic Solutions of Weakly Coupled Hamiltonian Systems

Subharmonic Solutions of Weakly Coupled Hamiltonian Systems

We prove the existence of an arbitrarily large number of subharmonic solutions for a class of weakly coupled Hamiltonian systems which includes the case when the Hamiltonian function is periodic in all of its variables and its critical points are non-degenerate. Our results are obtained through a ca...

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Veröffentlicht in:Journal of dynamics and differential equations 2023-09, Vol.35 (3), p.2337-2353
Hauptverfasser: Fonda, Alessandro, Toader, Rodica
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Critical point
Hamiltonian functions
Mathematical analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
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Zusammenfassung:We prove the existence of an arbitrarily large number of subharmonic solutions for a class of weakly coupled Hamiltonian systems which includes the case when the Hamiltonian function is periodic in all of its variables and its critical points are non-degenerate. Our results are obtained through a careful analysis of the dynamics of the planar components, combined with an application of a generalized version of the Poincaré–Birkhoff Theorem.
ISSN:1040-7294
1572-9222
DOI:10.1007/s10884-021-10106-1