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A branching method for studying stability of a solution to a delay differential equation.

Sibirskij Matematicheskij Zhurnal

A note on a nonlinear functional differential system with feedback control.

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

A note on the periodicity in difference equations

Archivum Mathematicum

A notion of boundedness for hyperfunctions and Massera type theorems

Banach Center Publications

For some classes of periodic linear ordinary differential equations and functional equations, it is known that the existence of a bounded solution in the future implies the existence of a periodic solution. In order to think on such phenomena for hyperfunction solutions to linear functional equations, we introduced a notion of bounded hyperfunctions, and translated the problems into the problems on analytic solutions to some equations in complex domains. In this article, after...

A predator-prey Gompertz model with time delay and impulsive perturbations on the prey.

Discrete Dynamics in Nature and Society

A predator-prey model in the chemostat with time delay.

International Journal of Differential Equations

A rigidity phenomenon for the Hardy-Littlewood maximal function

Studia Mathematica

The Hardy-Littlewood maximal function ℳ and the trigonometric function sin x are two central objects in harmonic analysis. We prove that ℳ characterizes sin x in the following way: Let $f\in {C}^{\alpha }\left(ℝ,ℝ\right)$ be a periodic function and α > 1/2. If there exists a real number 0 < γ < ∞ such that the averaging operator $\left({A}_{x}f\right)\left(r\right)=1/2r{\int }_{x-r}^{x+r}f\left(z\right)dz$ has a critical point at r = γ for every x ∈ ℝ, then f(x) = a + bsin(cx+d) for some a,b,c,d ∈ ℝ. This statement can be used to derive a characterization of trigonometric functions as those nonconstant...

Almost homoclinic solutions for a certain class of mixed type functional differential equations

Annales Polonici Mathematici

We shall be concerned with the existence of almost homoclinic solutions for a class of second order functional differential equations of mixed type: $q̈\left(t\right)+{V}_{q}\left(t,q\left(t\right)\right)+u\left(t,q\left(t\right),q\left(t-T\right),q\left(t+T\right)\right)=f\left(t\right)$, where t ∈ ℝ, q ∈ ℝⁿ and T>0 is a fixed positive number. By an almost homoclinic solution (to 0) we mean one that joins 0 to itself and q ≡ 0 may not be a stationary point. We assume that V and u are T-periodic with respect to the time variable, V is C¹-smooth and u is continuous. Moreover, f is non-zero, bounded, continuous and square-integrable....

Almost-periodic solution for BAM neural networks.

Surveys in Mathematics and its Applications

An epidemic model with a time delay in transmission

Applications of Mathematics

We study a mathematical model which was originally suggested by Greenhalgh and Das and takes into account the delay in the recruitment of infected persons. The stability of the equilibria are also discussed. In addition, we show that the introduction of a time delay in the transmission term can destabilize the system and periodic solutions can arise by Hopf bifurcation.

An optimal condition for the uniqueness of a periodic solution for linear functional differential systems.

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Analysis of a nonautonomous delayed predator-prey system with a stage structure for the predator in a polluted environment.

International Journal of Mathematics and Mathematical Sciences

Anti-periodic solutions for a class of third-order nonlinear differential equations with a deviating argument.

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Anti-periodic solutions for high-order cellular neural networks with time-varying delays.

Electronic Journal of Differential Equations (EJDE) [electronic only]

Anti-periodic solutions for recurrent neural networks without assuming global Lipschitz conditions.

Electronic Journal of Differential Equations (EJDE) [electronic only]

Bifurcation analysis for a delayed predator-prey system with stage structure.

Fixed Point Theory and Applications [electronic only]

Bifurcation analysis in a kind of fourth-order delay differential equation.

Discrete Dynamics in Nature and Society

Bifurcation analysis of a Kaldor-Kalecki model of business cycle with time delay.

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Bifurcation analysis on a delayed SIS epidemic model with stage structure.

Electronic Journal of Differential Equations (EJDE) [electronic only]

Bounded and periodic solutions of nonlinear integro-differential equations with infinite delay.

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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