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.
Type: Article
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)

Files in This Item:
File Description SizeFormat
GirardiMatzeuRendMat18.pdf428.08 kBAdobe PDFThumbnail
View/Open
Show full item record


CORE Recommender

Page view(s) 20

962
checked on Jul 6, 2022

Download(s) 50

329
checked on Jul 6, 2022

Google ScholarTM

Check


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.