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  4. Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics
  5. Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.18 (1986)
  6. Solutions of minimal period for Hamiltonian systems with quadratic growth at the origin and superquadratic at infinity
 
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Solutions of minimal period for Hamiltonian systems with quadratic growth at the origin and superquadratic at infinity

Girardi, Mario
•
Matzeu, Michele
1986
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ISSN
0049-4704
http://hdl.handle.net/10077/4970
  • Article

Abstract
Vengono presentate alcune tecniche basate sulla teoria dell'indice di Morse e su un'opportuna versione del principio di dualità di Clarke ed Ekeland per dare alcuni risultati sull'esistenza di soluzioni di periodo minimo prefissato di sistemi Hamiltoniani del tipo \[ \dot{x}=\omega_{i}y_{i}+\frac{\partial}{\partial x_{i}}\hat{H}(x,y),-\dot{y_{i}}=\omega_{i}x_{i}+\frac{\partial}{\partial y_{i}}\hat{H}(x,y)(i=1,...,N), \] \[ \textrm{dove}\:0<\omega_{1}\leq...\leq\omega_{N}\:\textrm{e}\hat{H}\epsilon C^{2}(\mathbf{R^{\textrm{2N}}\textrm{;}R\textrm{)}} \] è strettamente convessa ed ha un comportamento superquadratico.
Some techniques based on the Morse index theory and a suitable version of the duality principle by Clarke and Ekeland are presented here in order to give some results about the existence of periodic solutions with prescribed minimal period to Hamiltonian systems of the type \[ \dot{x}=\omega_{i}y_{i}+\frac{\partial}{\partial x_{i}}\hat{H}(x,y),-\dot{y_{i}}=\omega_{i}x_{i}+\frac{\partial}{\partial y_{i}}\hat{H}(x,y)(i=1,...,N), \] \[ \textrm{where}\:0<\omega_{1}\leq...\leq\omega_{N}\:\textrm{and}\hat{H}\epsilon C^{2}(\mathbf{R^{\textrm{2N}}\textrm{;}R\textrm{)}} \] is strictly convex and has a superquadratic behaviour.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
18 (1986)
Publisher
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source
Mario Girardi, Michele Matzeu, “Solutions of minimal period for Hamiltonian systems with quadratic growth at the origin and superquadratic at infinity”, in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 18 (1986), pp. 76-82.
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