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We use a modification of Krasnoselskii’s fixed point theorem due to Burton (see [Liapunov functionals, fixed points and stability by Krasnoselskii’s theorem, Nonlinear Stud. 9 (2002), 181–190], Theorem 3) to show that the totally nonlinear neutral differential equation with variable delay $x^{'} (t) = - a (t) h (x (t)) + c (t) x^{'} (t - g (t)) Q^{'} (x (t - g (t))) + G (t, x (t), x (t - g (t))),$ has a periodic solution. We invert this equation to construct a fixed point mapping expressed as a sum of two mappings such that one is compact and the other is a large contraction. We show that the mapping fits...

Existence of periodic solutions for neutral nonlinear differential equations with variable delay.

Hafsia, Deham, Ahcéne, Djoudi (2010)

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

Existence of Periodic Solutions for Nonlinear Neutral Dynamic Equations with Functional Delay on a Time Scale

Abdelouaheb Ardjouni, Ahcène Djoudi (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Let $𝕋$ be a periodic time scale. The purpose of this paper is to use a modification of Krasnoselskii’s fixed point theorem due to Burton to prove the existence of periodic solutions on time scale of the nonlinear dynamic equation with variable delay $x^{▵} (t) = - a (t) h (x^{σ} (t)) + c (t) x^{\tilde{▵}} (t - r (t)) + G (t, x (t), x (t - r (t)))$ , $t \in 𝕋$ , where $f^{▵}$ is the $▵$ -derivative on $𝕋$ and $f^{\tilde{▵}}$ is the $▵$ -derivative on $(i d - r) (𝕋)$ . We invert the given equation to obtain an equivalent integral equation from which we define a fixed point mapping written as a sum of a large contraction and a compact map. We show...

Existence of periodic solutions for second order delay differential equations with impulses.

Pan, Lijun (2011)

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

Existence of periodic solutions for second-order neutral differential equations.

Li, Yongjin (2005)

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

Existence of periodic solutions in totally nonlinear delay dynamic equations.

Adivar, M., Raffoul, Y. (2009)

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

Existence of periodic solutions of a delayed predator-prey system on time scales.

Yang, Dandan (2007)

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

Existence of positive periodic solution of a periodic cooperative model with delays and impulses.

Li, Yongkun, Xing, Wenya (2006)

International Journal of Mathematics and Mathematical Sciences

Existence of positive periodic solutions for delayed predator-prey patch systems with stocking.

Fang, Hui, Wang, Zhicheng (2006)

International Journal of Mathematics and Mathematical Sciences

Existence of positive periodic solutions for neutral functional differential equations.

Li, Zhixiang, Wang, Xiao (2006)

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

Existence of positive periodic solutions for non-autonomous functional differential equations.

Cheng, Sui Sun, Zhang, Guang (2001)

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

Existence of positive periodic solutions of higher-order functional difference equations

Xin-Ge Liu, Mei-Lan Tang (2014)

Applications of Mathematics

Based on the fixed-point theorem in a cone and some analysis skill, a new sufficient condition is obtained for the existence of positive periodic solutions for a class of higher-order functional difference equations. An example is used to illustrate the applicability of the main result.

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Existence of periodic orbits, set of global solutions and behavior near equilibrium for Volterra equations of retarded type.

Existence of periodic solution for first order nonlinear neutral delay equations.

Existence of periodic solutions for a class of even order differential equations with deviating argument.

Existence of periodic solutions for a delayed ratio-dependent three-species predator-prey diffusion system on time scales.

Existence of periodic solutions for first-order totally nonlinear neutral differential equations with variable delay

Existence of periodic solutions for neutral nonlinear differential equations with variable delay.

Existence of Periodic Solutions for Nonlinear Neutral Dynamic Equations with Functional Delay on a Time Scale

Existence of periodic solutions for second order delay differential equations with impulses.

Existence of periodic solutions for second-order neutral differential equations.

Existence of periodic solutions in totally nonlinear delay dynamic equations.

Existence of periodic solutions of a delayed predator-prey system on time scales.

Existence of positive periodic solution of a periodic cooperative model with delays and impulses.

Existence of positive periodic solutions for delayed predator-prey patch systems with stocking.

Existence of positive periodic solutions for neutral functional differential equations.

Existence of positive periodic solutions for non-autonomous functional differential equations.

Existence of positive periodic solutions of higher-order functional difference equations

Existence of positive periodic solutions to third-order delay differential equations.

Existence of three positive periodic solutions for differential systems with feedback controls on time scales.

Existence of triple positive periodic solutions of a functional differential equation depending on a parameter.

Existence theorem of periodic positive solutions for the Rayleigh equation of retarded type.

Currently displaying 21 – 40 of 40