Periodic solutions for periodic second-order differential equations with variable potentials

Periodic solutions of second-order differential equations with multiple delays

* Correspondence: [email protected] School of Mathematical Science and Computing Technology, Central South University, Changsha 410075, P. R. China Full list of author information is available at the end of the article Abstract By using the critical point theory and S index theory, we obtain a new result for the existence and multiplicity of periodic solutions for a class of second-order...

Periodic Solutions of Second-order Nonautonomous Impulsive Differential Equations

The main purpose of this paper is to study the existence of periodic solutions of second order impulsive differential equations with superlinear nonlinear terms. Our result generalizes one of Paul H. Rabinowitz’s existence results of periodic solutions of second order ordinary differential equations to impulsive cases. Mountain Pass Lemma is applied in order to prove our main results. AMS Subje...

Almost Periodic Solutions of Second Order Nonlinear Differential Equations with Almost Periodic Forcing

Unbounded Solutions and Periodic Solutions for Second Order Differential Equations with Asymmetric Nonlinearity

In this paper we will prove the coexistence of unbounded solutions and periodic solutions for the asymmetric oscillator ẍ+ f(ẋ) + ax − bx− = φ(t, x), where a and b are positive constants satisfying the nonresonant condition 1 √ a + 1 √ b / ∈ Q and φ(t, x) is 2π−periodic in the first variable and bounded.

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.