Periodic behaviour of nonlinear, second-order discrete dynamical systems

Periodic Solutions of Second-order Nonautonomous Dynamical Systems

Periodic solutions of second order non-autonomous singular dynamical systems

In this paper, we establish two different existence results of positive periodic solutions for second order non-autonomous singular dynamical systems. The first one is based on a nonlinear alternative principle of Leray–Schauder and the result is applicable to the case of a strong singularity as well as the case of a weak singularity. The second one is based on Schauder’s fixed point theorem an...

Multiple periodic solutions for superquadratic second-order discrete Hamiltonian systems

Some multiplicity results are obtained for periodic solutions of the nonautonomous superquadratic second-order discrete Hamiltonian systems Duðt 1Þ þ rF ðt; uðtÞÞ 1⁄4 0 8t 2 Z 0096-3 doi:10. q Sup Outsta * Co E-m Plea Com by using critical point theory, especially, a three critical points theorem proposed by Brezis and Nirenberg. 2007 Elsevier Inc. All rights reserved.

Multiple periodic solutions for second-order discrete Hamiltonian systems

By applying critical point theory, the multiplicity of periodic solutions to second-order discrete Hamiltonian systems with partially periodic potentials was considered. It is noticed that, in this paper, the nonlinear term is growing linearly and main results extend some present results. c ©2017 all rights reserved.

Nonlinear second-order dynamical systems on Riemannian manifolds: Damped oscillators

Linear as well as non-linear mathematical systems that exhibit an oscillatory behavior are ubiquitous in sciences and engineering. Such mathematical systems have been used to model the behavior of biological structures, such as the pulsating contraction of cardiac cells, as well as the behavior of electrical and mechanical components. Chaotic oscillators are currently being used in the secure t...