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We shall be concerned with the existence of almost homoclinic solutions for a class of second order functional differential equations of mixed type: $q ̈ (t) + V_{q} (t, q (t)) + u (t, q (t), q (t - T), q (t + T)) = f (t)$ , 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 of a diffusive mixed system with time delay and type III functional response.

Liu, Qiong (2008)

Discrete Dynamics in Nature and Society

Almost periodic solutions for a class of discrete systems with Allee-effect

Yongkun Li, Li Yang, Wanqin Wu (2014)

Applications of Mathematics

In this paper, using Mawhin's continuation theorem of the coincidence degree theory, we obtain some sufficient conditions for the existence of positive almost periodic solutions for a class of delay discrete models with Allee-effect.

Almost periodic solutions for higher-order Hopfield neural networks without bounded activation functions.

Zhang, Fuxing, Li, Ya (2007)

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

Almost periodic solutions of a discrete mutualism model with feedback controls.

Wang, Zheng, Li, Yongkun (2010)

Discrete Dynamics in Nature and Society

Almost periodic solutions of neutral impulsive systems with periodic time-dependent perturbed delays

Valéry Covachev, Zlatinka Covacheva, Haydar Akça, Eada Al-Zahrani (2003)

Open Mathematics

A neutral impulsive system with a small delay of the argument of the derivative and another delay which differs from a constant by a periodic perturbation of a small amplitude is considered. If the corresponding system with constant delay has an isolated ω-periodic solution and the period of the delay is not rationally dependent on ω, then under a nondegeneracy assumption it is proved that in any sufficiently small neighbourhood of this orbit the perturbed system has a unique almost periodic solution....

Almost periodic solutions with a prescribed spectrum of linear and quasilinear differential equations with almost periodic coefficients and constant time lag (Neutral differential equations)

Alexandr Fischer (2012)

Mathematica Bohemica

The paper is the extension of the author's previous papers and solves more complicated problems. Almost periodic solutions of a certain type of almost periodic linear or quasilinear systems of neutral differential equations are dealt with.

Almost sure exponential stability of delayed cellular neural networks.

Huang, Chuangxia, He, Yigang, Huang, Lihong (2007)

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

Almost sure exponential stability of neutral differential difference equations with damped stochastic perturbations.

Liao, Xiao Xin, Mao, Xuerong (1996)

Electronic Journal of Probability [electronic only]

Almost sure stability of linear Itô-Volterra equations with damped stochastic perturbations.

Appleby, John A.D. (2002)

Electronic Communications in Probability [electronic only]

Almost sure subexponential decay rates of scalar Itô-Volterra equations.

Appleby, John A.D. (2003)

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

Almost-periodic mild solutions to a class of partial functional-differential equations.

Aulbach, Bernd, Nguyen Van Minh (1998)

Abstract and Applied Analysis

Almost-periodic solution for BAM neural networks.

Jalab, H.A., Ibrahim, R.W. (2009)

Surveys in Mathematics and its Applications

Almost-periodic weak solutions of second-order neutral delay-differential equations with piecewise constant argument.

Wang, Li, Zhang, Chuanyi (2008)

Advances in Difference Equations [electronic only]

An abstract Cauchy problem for higher order functional differential inclusions with infinite delay

Tran Dinh Ke, Valeri Obukhovskii, Ngai-Ching Wong, Jen-Chih Yao (2011)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The existence results for an abstract Cauchy problem involving a higher order differential inclusion with infinite delay in a Banach space are obtained. We use the concept of the existence family to express the mild solutions and impose the suitable conditions on the nonlinearity via the measure of noncompactness in order to apply the theory of condensing multimaps for the demonstration of our results. An application to some classes of partial differential equations is given.

An abstract existence result and its applications.

Cheng, Sui Sun, Ju, Jian-She, Liu, Bin (2001)

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

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