Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4970
Title: Solutions of minimal period for Hamiltonian systems with quadratic growth at the origin and superquadratic at infinity
Authors: Girardi, Mario
Matzeu, Michele
Issue Date: 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.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
18 (1986)
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.
URI: http://hdl.handle.net/10077/4970
ISSN: 0049-4704
Appears in Collections:Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics vol.18 (1986)

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