Notes on Multiple Periodic Solutions for Second Order Hamiltonian Systems
In this paper, we study the multiplicity of periodic solutions for the second order Hamiltonian systems u ¨ + ∇ F ( t , u ) = 0 with the boundary condition u ( 0 ) - u ( T ) = u ˙ ( 0 ) - u ˙ ( T ) = 0 , where the potential F is either subquadratic k ( t )-concave or subquadratic μ ( t ) -convex. Ba...
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| Veröffentlicht in: | Qualitative theory of dynamical systems 2022-12, Vol.21 (4), Article 141 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper, we study the multiplicity of periodic solutions for the second order Hamiltonian systems
u
¨
+
∇
F
(
t
,
u
)
=
0
with the boundary condition
u
(
0
)
-
u
(
T
)
=
u
˙
(
0
)
-
u
˙
(
T
)
=
0
, where the potential
F
is either subquadratic
k
(
t
)-concave or subquadratic
μ
(
t
)
-convex. Based on the reduction method and a three-critical-point theorem due to Brezis and Nirenberg, we obtain the multiplicity results, which complement and sharply improve some related results in the literature. |
|---|---|
| ISSN: | 1575-5460 1662-3592 |
| DOI: | 10.1007/s12346-022-00673-z |