Periodic solutions for some nonautonomous second-order systems

Periodic Solutions of Second-order Nonautonomous Dynamical Systems

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...

Existence of Infinitely Many Periodic Solutions for Second-order Nonautonomous Hamiltonian Systems

By using minimax methods and critical point theory, we obtain infinitely many periodic solutions for a second-order nonautonomous Hamiltonian systems, when the gradient of potential energy does not exceed linear growth.

Infinitely Many Periodic Solutions for Nonautonomous Sublinear Second-Order Hamiltonian Systems

and Applied Analysis 3 Our main result is the following theorem. Theorem 1.1. Suppose that F t, x satisfies assumptions (A) and 1.7 . Assume that lim sup r→ ∞ inf x∈RN,|x| r |x|−2α ∫T 0 F t, x dt ∞, 1.8 lim inf R→ ∞ sup x∈RN,|x| R |x|−2α ∫T 0 F t, x dt −∞. 1.9

Existence of Square-mean Almost Periodic Mild Solutions to Some Nonautonomous Stochastic Second-order Differential Equations

In this paper we use the well-known Schauder fixed point principle to obtain the existence of square-mean almost periodic solutions to some classes of nonautonomous second order stochastic differential equations on a Hilbert space.