Study of the Periodic or Nonnegative Periodic Solutions of Functional Differential Equations via Krasnoselskii–Burton’s Theorem

Mesmouli, Mouataz Billah; Ardjouni, Abdelouaheb; Djoudi, Ahcéne

doi:10.1007/s12591-014-0235-5

Cited by 2 publications

(1 citation statement)

References 16 publications

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“…In [5], Burton introduced the concept of a large contraction and proved an extension of the Krasnosel'skiĭ fixed point theorem to the case in which the fixed point operator is expressed as the sum of a compact operator and a large contraction. Burton's theorem has proved to be quite useful in the study of both delay differential equations and delay Volterra difference equations [1, 4-6, 10, 15-18], as well as other functional or fractional equations [7][8][9]12].…”

Section: Introductionmentioning

confidence: 99%

The large contraction principle and existence of periodic solutions for infinite delay Volterra difference equations

Eloe¹,

Jonnalagadda²,

Raffoul³

2019

Turk J Math

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In this article, we establish sufficient conditions for the existence of periodic solutions of a nonlinear infinite delay Volterra difference equation: ∆x(n) = p(n) + b(n)h(x(n)) + n ∑ k=−∞ B(n, k)g(x(k)). We employ a Krasnosel'skiĭ type fixed point theorem, originally proved by Burton. The primary sufficient condition is not verifiable in terms of the parameters of the difference equation, and so we provide three applications in which the primary sufficient condition is verified.

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Section: Introductionmentioning

confidence: 99%

The large contraction principle and existence of periodic solutions for infinite delay Volterra difference equations

Eloe¹,

Jonnalagadda²,

Raffoul³

2019

Turk J Math

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Existence of periodic solutions and stability for a nonlinear system of neutral differential equations

Li,

Chen

2024

ejde

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In this article, we study the existence and uniqueness of periodic solutions, and stability of the zero solution to the nonlinear neutral system $$ \frac{d}{dt}x(t)=A(t)h\big(x(t-\tau_1(t))\big)+\frac{d}{dt}Q\big(t,x(t-\tau_2(t))\big) +G\big(t,x(t),x(t-\tau_2(t))\big). $$ We use integrating factors to transform the neutral differential equation into an equivalent integral equation. Then we construct appropriate mappings and employ Krasnoselskii's fixed point theorem to show the existence of a periodic solution. We also use the contraction mapping principle to show the existence of a unique periodic solution and the asymptotic stability of the zero solution. Our results generalize the corresponding results in the existing literature. An example is given to illustrate our results.For more information see https://ejde.math.txstate.edu/Volumes/2024/21/abstr.html

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Study of the Periodic or Nonnegative Periodic Solutions of Functional Differential Equations via Krasnoselskii–Burton’s Theorem

Cited by 2 publications

References 16 publications

The large contraction principle and existence of periodic solutions for infinite delay Volterra difference equations

The large contraction principle and existence of periodic solutions for infinite delay Volterra difference equations

Existence of periodic solutions and stability for a nonlinear system of neutral differential equations

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