On the Boundedness of Solution of the Second Order Ordinary Differential Equation with Involution

Authors

  • Allaberen Ashyralyev Department of Mathematics, Near East University, Nicosia, Mersin 10, Turkey. & Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow 117198, Russian Federation. & Institute of Mathematics and Mathematical Modeling, 050010, Almaty, Kazakhstan. Author
  • Barez Abdalmohammed Department of Mathematics, Near East University, Nicosia, Mersin 10, Turkey. Author

DOI:

https://doi.org/10.17656/jzs.10824

Keywords:

Ordinary differential equation with involution, Stability, Boundedness, Existence and uniqueness

Abstract

In the present paper, the initial value problem for the second order ordinary differential equation with involution is investigated. We obtain equivalent initial value problem for the fourth order ordinary differential equations to the initial value problem for second order linear differential equations with involution. Theorem on stability estimates for the solution of the initial value problem for the second order ordinary linear differential equation with involution is proved. Theorem on existence and uniqueness of bounded solution of initial value problem for second order ordinary nonlinear differential equation with involution is established.

References

C. E. Falbo. "Idempotent differential equations". Journal of Interdisciplinary Mathematics 6(3), 279–289 (2003). DOI: https://doi.org/10.1080/09720502.2003.10700346

R. Nesbit. "Delay Differential Equations for Structured Populations". Structured Population Models in Marine,Terrestrial and Freshwater Systems. (1997).

A. Ashyralyev and A. S. Erdogan. "Well-Posedness of a Parabolic Equation with Involution". Numerical Functional Analysis and Optimization. Vol. 38, No. 10, pp. 1295–1304. (2017). DOI: https://doi.org/10.1080/01630563.2017.1316997

M. Ashyraliyev, M. Ashyralyyeva, and A. Ashyralyev. "A note on the hyperbolic-parabolic identification problem with involution and Dirichlet boundary condition". Bullition of the Karaganda Univesity-Mathematics. Vol. 99, No. 3, pp. 120–129. (2020). DOI: https://doi.org/10.31489/2020M3/120-129

D. Przeworska-Rolewicz. "Equations with Transformed Argument". Algebraic Approach, Amsterdam, Warszawa. (1997).

J. Wiener. "Generalized Solutions of Functional Differential Equations". Singapore New Jersey, London Hong Kong. (1993). DOI: https://doi.org/10.1142/1860

A.Cabada and F. Tojo. "Differential Equations with Involutions". Atlantis Press. (2015). DOI: https://doi.org/10.2991/978-94-6239-121-5

A. Ashyralyev and P. E. Sobolevskii. "New Difference Schemes for Partial Differential Equations". Birkhäuser Verlag, Basel, Boston, Berlin. (2004). DOI: https://doi.org/10.1007/978-3-0348-7922-4

A. Ashyralyev. "Computational Mathematics". Textbook-The South Kazakhstan State University Named after M. Auezovuku Printing House, Chimkent. (2013).

Published

2020-12-20

How to Cite

On the Boundedness of Solution of the Second Order Ordinary Differential Equation with Involution. (2020). Journal of Zankoy Sulaimani - Part A, 22(2), 237-246. https://doi.org/10.17656/jzs.10824