scholarly journals A systematic approach to nonresonance conditions for periodically forced planar Hamiltonian systems

2021 ◽  
Author(s):  
Christian Fabry ◽  
Alessandro Fonda
Keyword(s):  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Systematic Approach ◽  
General Setting ◽  
Differential Systems ◽  
Periodic Perturbations ◽  
Existence And Multiplicity

AbstractIn the first part of the paper we consider periodic perturbations of some planar Hamiltonian systems. In a general setting, we detect conditions ensuring the existence and multiplicity of periodic solutions. In the second part, the same ideas are used to deal with some more general planar differential systems.

scholarly journals Periodic solutions and their stability for some perturbed Hamiltonian systems

2020 ◽  
Vol 18 (01) ◽  
pp. 2150013
Author(s):  
Juan L. G. Guirao ◽  
Jaume Llibre ◽  
Juan A. Vera ◽  
Bruce A. Wade
Keyword(s):  
Dynamical Systems ◽  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Degree Of Freedom ◽  
Averaging Theory ◽  
Differential Systems ◽  
Type Of Stability

We deal with non-autonomous Hamiltonian systems of one degree of freedom. For such differential systems, we compute analytically some of their periodic solutions, together with their type of stability. The tool for proving these results is the averaging theory of dynamical systems. We present some applications of these results.

Existence and multiplicity of periodic solutions for some second order differential systems with p(t)-Laplacian

2013 ◽  
Vol 63 (6) ◽  
Author(s):  
Liang Zhang ◽  
X. Tang
Keyword(s):  
Hamiltonian System ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Existence Theorems ◽  
Point Theory ◽  
Least Action Principle ◽  
Differential Systems ◽  
Least Action ◽  
Existence And Multiplicity ◽  
The Least Action Principle

AbstractIn this paper, we deal with the existence and multiplicity of periodic solutions for the p(t)-Laplacian Hamiltonian system. Some new existence theorems are obtained by using the least action principle and minmax methods in critical point theory, and our results generalize and improve some existence theorems.

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