Periodic solution of second-order Hamiltonian systems with a change sign potential on time scales.
In this paper, we are concerned with a delayed multispecies competition predator-prey dynamic system with Beddington-DeAngelis functional response. Some sufficient conditions which guarantee the existence of a positive periodic solution for the system are obtained by applying the Mawhin coincidence theory. The interesting thing is that the result is related to the delays, which is different from the corresponding ones known from literature (the results are delay-independent).
In this paper, we study the existence of periodic solutions to a class of functional differential system. By using Schauder's fixed point theorem, we show that the system has aperiodic solution under given conditions. Finally, four examples are given to demonstrate the validity of our main results.
By means of the Krasnoselskii fixed piont theorem, periodic solutions are found for a neutral type delay differential system of the form
We consider first order periodic differential inclusions in . The presence of a subdifferential term incorporates in our framework differential variational inequalities in . We establish the existence of extremal periodic solutions and we also obtain existence results for the “convex” and “nonconvex”problems.
We consider first order neutral functional differential equations with multiple deviating arguments of the form . By using coincidence degree theory, we establish some sufficient conditions on the existence and uniqueness of periodic solutions for the above equation. Moreover, two examples are given to illustrate the effectiveness of our results.