jzs-10824

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

 Allaberen Ashyralyev1, 2, 3 and Barez Abdalmohammed1

1 Department of Mathematics, Near East University, Nicosia, Mersin 10, Turkey.

2 Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St,Moscow 117198, Russian Federation.

3 Institute of Mathematics and Mathematical Modeling, 050010, Almaty,Kazakhstan.

*Corresponding author’s e-mail:: barez.osman@gmail.com and allaberen.ashyralyev@neu.edu.tr

Original: 7 August 2020        Revised: 14 September 2020        Accepted: 26 September 2020        Published online: 20 December 2020  

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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.

Key Words: Ordinary differential equation with involution, Stability, Boundedness, Existence and uniqueness

References

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