Nonlinear second-order delay differential equation
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Publication date: 29.03.2019
Technical Transactions, 2019, Volume 3 Year 2019 (116), pp. 141 - 148
https://doi.org/10.4467/2353737XCT.19.038.10212Authors
Nonlinear second-order delay differential equation
The aim of this paper is to prove the theorem on the existence and uniqueness of the classical solution of the initial-boundary value problem for a nonlinear second-order delay differential equation. For this purpose, we apply the Banach contraction principle and the Bielecki norm. The paper is based on publications [1–7] and is a generalisation of publication [6].
Streszczenie
Nieliniowe równanie różniczkowe rzędu drugiego z opóźnieniem
W artykule udowodniono twierdzenie o istnieniu i jednoznaczności klasycznego rozwiązania zagadnienia początkowo-brzegowego dla nieliniowego równania różniczkowego rzędu drugiego z opóźnieniem. W tym celu stosowane jest twierdzenie Banacha o punkcie stałym i norma Bieleckiego. Artykuł bazuje na publikacjach [1–7] i jest uogólnieniem publikacji [6].
[1] Balachandran K., Byszewski L., Kim J. K., Cauchy problem for second order functional differential equations and fractional differential equations, Nonlinear Functional Analysis and Applications, 2019 (in press).
[2] Jankowski T., Functional differential equations of second order, Bull. Belg. Math. Soc. 10, 2003, 291–298.
[3] Li Long Tu, Zhi Cheng Wang, Xiang Zheng Qian, Boundary value problems for second order delay differential equations, Appl. Math. Mech. (English Ed.) 14.6, 1993, 573–580.
[4] Lin Xiao Ning, Xu Xiao Jie, Singular semipositive boundary value problems for second-order delay differential equations, Acta Math. Sci. Ser A (Chin. Ed.) 25.4, 2005, 49–502.
[5] Liu B., Positive solutions of second-order three-point boundary value problems with change of sign, Comput. Math. Appl. 47. 8-9, 2004, 1351–1361.
[6] Skóra L., Second order delay differential equations, Monograph of the Cracow University of Technology, Collective work edited by Jan Koroński, Cracow 2017, 215–229.
[7] Wang Jie, Liu Bing, Positive solutions of boundary value problems for second-order delay differential equations, Ann. Differential Equations 23.2, 2007, 199–208.
Information: Technical Transactions, 2019, Volume 3 Year 2019 (116), pp. 141 - 148
Article type: Original article
Titles:
Nonlinear second-order delay differential equation
Nonlinear second-order delay differential equation
Institute of Mathematics, Faculty of Physics, Mathematics and Computer Science, Cracow University of Technology
Published at: 29.03.2019
Article status: Open
Licence: None
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