The existence of periodic and subharmonic solutions to subquadratic discrete Hamiltonian systems

Abstract

In this paper, by using critical point theory, we establish some results for the existence of periodic and subharmonic solutions to subquadratic discrete Hamiltonian systems.

Applications of Clark duality to periodic solutions with minimal period for discrete Hamiltonian systems

“…On the one hand, with the sharp development of difference equations' studies, difference equations have been widely used as mathematical models to describe real life situations in probability theory, matrix theory, electrical circuit analysis, combinatorial analysis, number theory, psychology and sociology, and etc. On the other hand, the critical point theory has been widely used to study the existence of periodic solutions, subharmonic solutions and boundary value problems to difference equations, for example, Guo, Yu and Zhou [16][17][18]20] have done many excellent work on it by using critical point theory. In view of above reasons, we will devote ourselves to looking for periodic solutions having minimal period for (1.1).…”

Periodic Solutions for Subquadratic Discrete Hamiltonian Systems

“…Therefore, the problem of finding the T-periodic solution for (1.1) is reduced to the one of seeking the critical point of functional F. Next, we construct a variational structure by using the operator theory which is different from the one in [9,10,13].…”

Periodic solutions for discrete p ( k ) $p(k)$ -Laplacian systems with partially periodic potential

“…In [1,2], Guo and Yu developed a new method to study the existence and multiplicity of periodic and subharmonic solutions of the second order difference equation via variational methods. In 2005, Zhou et al [3] applied the same approach for subharmonic solutions of a class of subquadratic Hamiltonian systems. Here we also point out the contribution of Mawhin [4,5] in the study of second order nonlinear difference systems with ϕ-Laplacian and periodic potential by using critical point theory.…”