in this paper, we investigate the generalizedhyers--ulam stability of the functional equation

In this work we demonstrate how to derive the Kohn-Sham equations of time-dependent current-density functional theory from a generating action functional defined on a Keldysh time contour. These Kohn-Sham equations contain an exchange-correlation contribution to the vector potential. For this quantity we derive an integral equation. We further derive an integral equation for its functional deri...

Verifiable criteria are established for the permanence and existence of positive periodic solutions of a delayed discrete predator-prey model with monotonic functional response. It is shown that the conditions that ensure the permanence of this system are similar to those of its corresponding continuous system. And the investigations generalize some well-known results. In particular, a more acc...

Let ω > 0 be a constant. Suppose that {tk}∞k=−∞ is an increasing two-sided sequence and there exists a positive integer q such that tk+q = tk + ω for all k. Define PCω to be the space of all ω-periodic functions ψ : R→ R which are continuous for t 6= tk, are continuous from the left for t ∈ R and have possible discontinuities of the first kind at points t = tk; that is, the limit from the right...

By using a continuation theorem of Mawhin's coincidence degree , studied a periodic predator-prey system with dispersal and semi-ratio-functional response, sufficient conditions are obtained for the existence of positive periodic solution for the system.

This paper is concerned with a stochastic predator-prey model with Beddington DeAngelis functional response. The existence of the global solution and the ultimate boundedness of moments of the solution are proved. Moreover, we also estimate the average in time of the solution.

In this paper we derive some results to ensure the global stability of a predator-prey system. The results cover most of the models which have been proposed in the ecological literature for predator-prey systems. The first result is very geometric and it is very easy to check from the graph of prey and predator isoclines. The second one is purely algebraic, however, it covers the defects of the...

and Applied Analysis 3 To the best of the authors’ knowledge, for the nonautonomous case of predatorprey systems with two predators which consume immature prey and stage structure for prey, whether one could obtain the sufficient and necessary conditions which insure the permanence of the system or not is still an open problem. The aim of this paper is, by further developing the analysis techni...