Three periodic solutions to an eigenvalue problem for a class ofsecond‐order Hamiltonian systems

Abstract

We establish a multiplicity result to an eigenvalue problem related to second-order Hamiltonian systems. Under new assumptions, we prove the existence of an open interval of positive eigenvalues in which the problem admits three distinct periodic solutions

Multiple periodic solutions for second order systems with changing sign potential

“…We mention finally another interesting result on the topic recently obtained by Cordaro in [3] where the author proves the existence of at least three periodic solutions for system (S λ ). We notice that in the previous results it is not known whether λ can be taken equal to 1.…”

Three periodic solutions for perturbed second order Hamiltonian systems

“…All of the papers quoted above consider the problem without the perturbation term ∇G. We also note that, instead of [3,5], our multiplicity result is proved without assuming the positive definiteness of the matrix A(·) in [0, T ].…”

“…Focusing our attention on those ones which carried out their studies about the three periodic solutions, we cite Tang and Wu [9][10][11]. More recently other contributions to this topic has been given by Cordaro in [3] and Faraci in [5,6]. However, at our best knowledge, there are not many results of the type of Theorem 3.1 proposed here.…”

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.…”