Existence of periodic solutions in predator–prey and competition dynamic systems

In this paper, we systematically explore the periodicity of some dynamic equations on time scales, which incorporate as special cases many population models (e.g., predator–prey systems and competition systems) in mathematical biology governed by differential equations and difference equations. Easily verifiable sufficient criteria are established for the existence of periodic solutions of such dynamic equations, which generalize many known results for continuous and discrete population models when the time scale is chosen as or , respectively. The main approach is based on a continuation theorem in coincidence degree theory, which has been extensively applied in studying existence problems in differential equations and difference equations but rarely applied in dynamic equations on time scales. This study shows that it is unnecessary to explore the existence of periodic solutions of continuous and discrete population models in separate ways. One can unify such studies in the sense of dynamic equations on general time scales.     

Periodic solutions of neutral nonlinear system of differential equations with functional delay

We study the existence of periodic solutions of the nonlinear neutral system of differential equations of the form

     

Periodic solutions of the third order functional differential equations

We obtain sufficient conditions for the existence of periodic solutions of the following third order nonlinear functional differential equations

     

Existence of positive, negative and sign-changing periodic solutions for a class of integral equations

In this paper, the simultaneous existence of positive, negative and sign-changing periodic solutions for a class of integral equations of the form

     

Planar nonautonomous polynomial equations II. Coinciding sectors

We give a few sufficient conditions for the existence of periodic solutions of the equation where aj's are complex-valued. We prove the existence of one up to two periodic solutions and heteroclinic ones.     

Periodic solutions of Duffing equations with semi-quadratic potential and singularity

In this paper, we deal with the existence of periodic solutions of the second order differential equations x^″+g(x)=p(t) with singularity. We prove that the given equation has at least one periodic solution when g(x) has singularity at origin, satisfies