Periodic solutions of second order Hamiltonian systems with nonlinearity of general linear growth

1 January 2021

journal article
research article
Published by University of Szeged in Electronic Journal of Qualitative Theory of Differential Equations

No. 27,p. 1-19
https://doi.org/10.14232/ejqtde.2021.1.27

Abstract

In this paper we consider a class of second order Hamiltonian system with the nonlinearity of linear growth. Compared with the existing results, we do not assume an asymptotic of the nonlinearity at infinity to exist. Moreover, we allow the system to be resonant at zero. Under some general conditions, we will establish the existence and multiplicity of nontrivial periodic solutions by using the Morse theory and two critical point theorems.

Keywords

This publication has 29 references indexed in Scilit:

Some notes on a superlinear second order Hamiltonian system
manuscripta mathematica, 2016
Periodic solutions of second order superquadratic Hamiltonian systems with potential changing sign (II)
Journal of Differential Equations, 2005
Periodic solutions of second order superquadratic Hamiltonian systems with potential changing sign (I)
Journal of Differential Equations, 2005
Index theory, nontrivial solutions, and asymptotically linear second-order Hamiltonian systems
Journal of Differential Equations, 2005
Nonlinear differential problems and Morse theory
Nonlinear Analysis, 1997
Critical point theory for asymptotically quadratic functionals and applications to problems with resonance
Nonlinear Analysis, 1997
Nontrivial periodic solutions for strong resonance Hamiltonian systems
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 1997
Periodic solutions of asymptotically linear dynamical systems
Nonlinear Differential Equations and Applications NoDEA, 1994
Duality and Perturbation Methods in Critical Point Theory
Published by Cambridge University Press (CUP) ,1993
Infinite Dimensional Morse Theory and Multiple Solution Problems
Published by Springer Science and Business Media LLC ,1993