New existence of periodic solutions for second order non-autonomous Hamiltonian systems

Abstract

By using mountain pass theorem and local link theorem, some existence theorems are obtained for periodic solutions of second order non-autonomous Hamiltonian systems under local superquadratic condition and other suitable conditions.

Periodic Solutions for Second Order Hamiltonian Systems with Impulses via the Local Linking Theorem

“…By applying a local linking theorem, we establish the new criterion to guarantee that this impulsive Hamiltonian system has at least one nontrivial T-periodic solution under local superquadratic condition. This result generalizes and improves some existing results in the known literature.(A2) There exists 2 < < +∞ such that lim inf | | → +∞ ( ( , )/| | ) > 0, uniformly in ∈ R.In recent paper [25], Zhang and Tang had obtained some results of the nontrivial T-periodic solutions under much weaker assumptions instead of (A1) and (A2).…”

“…Recently, applying the local linking theorem (see [26]), the works in [27][28][29][30] obtained the existence of periodic solutions or homoclinic solutions with (3) superquadratic condition under different systems. As shown in [25], condition (B2) is a local superquadratic condition; this situation has been considered only by a few authors.…”

“…Motivated by papers [24,25,31], in this paper, we aim to consider problem (1) under local superquadratic condition via a version of the local linking theorem (see [26]). In particular, the impulsive function satisfies a kind of new superquadratic condition which is different from that in the known literature.…”

“…In recent paper [25], Zhang and Tang had obtained some results of the nontrivial T-periodic solutions under much weaker assumptions instead of (A1) and (A2).…”

Multiple Periodic Solutions for Perturbed Second-Order Impulsive Hamiltonian Systems

“…Background information and applications of Hamiltonian systems can be found for example in [16,28,31,37]. The monographs [29,32] have inspired a great deal of work on the existence and multiplicity of periodic solutions for Hamiltonian systems using variational techniques; for example, see [9,10,11,13,14,15,18,19,24,25,26,36,38,40,42,43,45] and the references therein.…”