Existence of periodic solutions for some second order quasi-linear Hamiltonian systems

Periodic Solutions of Second Order Hamiltonian Systems

We provide sufficient conditions for the existence of periodic solutions of the second order Hamiltonian system −x′′ − λx = εV ′ x (t, x) , where ε is a small parameter, x ∈ R and V (t, x) is 2π-periodic in t. Moreover we provide two applications.

Existence of Multiple Periodic Solutions for Second-order Discrete Hamiltonian Systems with Partially Periodic Potentials

In this article, we use critical point theory to obtain multiple periodic solutions for second-order discrete Hamiltonian systems, when the nonlinearity is partially periodic and its gradient is linearly and sublinearly bounded.

Existence and multiplicity of periodic solutions for a class of second-order Hamiltonian systems

In this paper, we study the existence and multiplicity of periodic solutions of the following second-order Hamiltonian systems ẍ(t) + V ′(t, x(t)) = 0, where t ∈ R, x ∈ R and V ∈ C(R × R ,R). By using a symmetric mountain pass theorem, we obtain a new criterion to guarantee that second-order Hamiltonian systems has infinitely many periodic solutions. We generalize and improve recent results fro...

On the existence of minimal periodic solutions for a class of second-order Hamiltonian systems

Multiplicity results for an eigenvalue second-order Hamiltonian system are investigated. Using suitable critical points arguments, the existence of an exactly determined open interval of positive eigenvalues for which the system admits at least three distinct periodic solutions is established. Moreover, when the energy functional related to the Hamiltonian system is not coercive, an existence r...

Existence of periodic solutions for a class of second order Hamiltonian systems