A nonautonomous semiratio-dependent predator-prey systemwith nonmonotonic functional responses is investigated. For general nonautonomous case, positive invariance, permanence, and globally asymptotic stability for the system are studied. For the periodic (almost periodic) case, sufficient conditions for existence, uniqueness, and stability of a positive periodic (almost periodic) solution are ...

This paper deals with the asymptotic behaviour of the solutions of linear initial boundary value problems with constant coefficients on the half-line and on finite intervals. We assume that the boundary data are periodic in time and we investigate whether the solution becomes time-periodic after sufficiently long time. Using the Fokas’ transformation method, we show that for the linear Schrödin...

We investigate the existence of the periodic solutions of a nonlinear integro-differential system with piecewise alternately advanced and retarded argument of generalized type, in short DEPCAG; that is, the argument is a general step function. We consider the critical case, when associated linear homogeneous system admits nontrivial periodic solutions. Criteria of existence of periodic solution...

We consider a ring of identical neurons with delayed nearest neighborhood inhibitory interaction. Under general conditions, such a network has a slowly oscillatory synchronous periodic solution which is completely characterized by a scalar delay differential equation with negative feedback. Despite the fact that the slowly oscillatory periodic solution of the scalar equation is stable, we show ...

Problems of Nehari type are studied for matrix valued k-variable almost periodic Wiener functions: Find contractive k-variable almost periodic Wiener functions having prespeciied Fourier coeecients with indices in a given halfspace of R k. We characterize the existence of a solution, give a construction of the solution set, and exhibit a particular solution that has a certain maximizing propert...

In this paper, the existence and uniqueness of periodic solution of first order impulsive differential equation is investigated on the Banach space PC(J) using the new method of iterative analysis which is introduced by Mengxing He and Anping Liu in the paper[9]. Base on the iterative sequence of the equation, we obtain the existence and uniqueness of periodic solution of first order impulsive ...

By applying the Horn’s fixed point theorem, we prove the existence of T0-periodic PC-mild solution of impulsive periodic systems when PC-mild solutions are ultimate bounded.

In this paper, periodic solution of impulsive Lotka-Volterra recurrent neural networks with delays is studied. Using the continuation theorem of coincidence degree theory and analysis techniques, we establish criteria for the existence of periodic solution of impulsive Lotka-Volterra recurrent neural networks with delays.

In this paper, we study the asymptotic behavior of the solution of a semilinear problem and of a Stokes problem, with periodic data, when the size of the domain increases. In particular, we prove exponential convergence to the solution of the corresponding problem with periodic boundary conditions.