Existence and uniqueness of positive periodic solution for nonlinear second order delay differential equations

• Autorzy: Bellour, Azzeddine , Benhiouna, Salah , Amiar, Rachida
• Języki publikacji: EN

Abstrakty

EN

This work is concerned with the following nonlinear second order delay differential equations x′′(t)+p(t)x′(t)+q(t)x(t) = f(t, x(t), x(t−τ (t)), x′(t−τ (t))), t ∈ R, which includes many key second order delay differential equations that arise in nonlinear analysis and its applications. We use Perov’s fixed point theorem to prove the existence and uniqueness of periodic solutions for second order delay differential equations. Our results are obtained under general assumptions.

Słowa kluczowe

EN

Perov’s fixed point; second order delay differential; equations; periodic solution

• Czasopismo: Fasciculi Mathematici
• Rocznik: 2024
• Tom: nr 67
• Strony: 13--23
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Bellour, Azzeddine

• Laboratory of Applied Mathematics and Didactics, Ecole Normale Supérieure de Constantine, Constantine-Algeria,

autor

Benhiouna, Salah

• Department of Mathematics, Ecole Normale Supérieure de Skikda,
• Laboratory of Applied Mathematics and Didactics, Ecole Normale Supérieure de Constantine, Constantine-Algeria

autor

Amiar, Rachida

• Department of Mathematics, Université Badji Mokhtar, Annaba-Algeria,

Bibliografia

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• [3] Aghajani A., Djoudi A., The existence of periodic solutions for a second order nonlinear neutral differential equation with functional delay, Electron. J. Qual. Theory Differ. Equ., (31)(2) (2012), 1-9.
• [4] Aghajani A., Djoudi A., Periodic solutions for a second-order nonlinear neutral differential equation with variable delay, Electron. J. Differential Equations, 11(128) (2011), 1072-6691.
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• [6] Bica A. M., Mureşan S., Parameter dependence of the solution of a delay integro-differential equation arising in infectious diseases, Fixed Point Theory, 6 (2005), 79-89.
• [7] Egri E., A boundary value problem for a system of iterative functional-differential equations, Carpathian J. Math., 24(1) (2008), 23-36.
• [8] Freedman H. I., Wu J., Periodic solutions of single-species models with periodic delay, SIAM J. Math. Anal., 23(2) (1992), 689-701.
• [9] Kuang Y., Delay Differential Equations with Application in Population Dynamics, Academic Press, New York, 1993.
• [10] Liu Y., Ge W., Positive periodic solutions of nonlinear Duffing equations with Delay and variable coefficients, Tamsui Oxf. J. Math. Sci., 20(2) (2004), 235-255.
• [11] Perov A. I., Kibenko A. V., On a general method to study the boundary value problems, Iz. Akod. Nank., 30(1966), 249-264.
• [12] Wang Y., Lian H., Ge W., Periodic solutions for a second nonlinear functional differential equation, Appl. Math. Lett., 20(2) (2007), 110-115.

Identyfikatory

DOI

10.21008/j.0044-4413.2024.0002