Non-autonomous second order Hamiltonian systems

Abstract

We study the existence of periodic solutions for a second order nonautonomous dynamical system containing variable kenetic energy terms. Our assumptions balance the interaction between the kenetic energy and the potential energy with neither one dominating the other. We study sublinear problems and the existence of non-constant solutions.

Existence and multiplicity of periodic solutions and subharmonic solutions for a class of elliptic equations

“…In the past, a series of existence results for periodic solution have been obtained in the literatures (see [1,2,8,13,20,21] and their references). But the widely used tool is either the various fixed point theorem or cone theory.…”

Rotating periodic solutions for asymptotically linear second‐order Hamiltonian systems with resonance at infinity

“…The existence of periodic solutions for second‐order Hamiltonian systems has been extensively studied in the past 30 years. Some existence and multiplicity results for periodic solutions were obtained by minimax methods and Morse theory under some suitable solvability conditions, such as the subquadratic potential conditions (see previous studies) and the references therein), the superquadratic potential conditions (see previous studies) and the references therein), and the asymptotically quadratic potential conditions (see previous studies) and the references therein).…”

Some notes on a superlinear second order Hamiltonian system

“…Because of the variational structure, direct methods as well as min-max methods of critical point theory have been widely exploited in several papers (see for example [9]- [23], [29], [32], [33], [35]- [55], [57]) with the aim of establishing different existence and multiplicity results of periodic solutions of problem (1.1).…”