Periodic non-autonomous second-order dynamical systems

Periodic solutions of second order non-autonomous singular dynamical systems

In this paper, we establish two different existence results of positive periodic solutions for second order non-autonomous singular dynamical systems. The first one is based on a nonlinear alternative principle of Leray–Schauder and the result is applicable to the case of a strong singularity as well as the case of a weak singularity. The second one is based on Schauder’s fixed point theorem an...

Periodic solutions to non-autonomous second-order systems

where x = (x1, . . . , xn), V (t, x) = (v1(t, x), . . . , vn(t, x)) ∈ C(R× Rn,Rn) is periodic of period T in the t variable, and μ is a constant. The existence of solutions of (1.1) has been studied by many researchers, see Mawhin andWillem [1] and the references therein. The variational method has beenmostly used to prove the existence of solutions of (1.1). Fixed point theorems such as Rothe’...

Periodic Solutions of Second Order Non-autonomous Differential Systems

We study the existence of nonnegative solutions for second order nonlinear differential systems with periodic boundary conditions. In this class of problems, where the associated Green’s function may take on negative values, and the nonlinear term is allowed to be singular. Our method is based on the Guo-Krasnosel’skii fixed point theorem of cone expansion and compression type, involving a new ...

Periodic Solutions of Second-order Nonautonomous Dynamical Systems

Duality Mappings and the Existence of Periodic Solutions for Non-autonomous Second Order Systems

is a vector version of p-Laplacian operator. In order to say what we understand by solution for the problem (1.1), (1.2) we remind some basic results concerning the W 1,p T -spaces. Let C T be the space of indefinitely differentiable T -periodic functions from R to R . We denote by 〈·, ·〉 the inner product on R and by ‖ · ‖, the norm generated by this inner product (the same meaning is applied ...