Estimation of the integral funnel for solutions of equations of perturbed motion with uncertain parameters

Anatoliy Martynyuk; Ivanka Stamova; Yulya Martynyuk–Chernienko; Anatoliy Martynyuk; Ivanka Stamova; Yulya Martynyuk–Chernienko

doi:10.3934/math.2025959

AIMS Mathematics

2025, Volume 10, Issue 9: 21581-21594. doi: 10.3934/math.2025959

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Estimation of the integral funnel for solutions of equations of perturbed motion with uncertain parameters

1.
S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterov str. 03057, Kiev-57, Ukraine
2.
Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA

Received: 27 May 2025 Revised: 27 July 2025 Accepted: 08 September 2025 Published: 17 September 2025
MSC : 34A34, 34B09, 34B15

In this article, for scalar nonlinear equations with uncertain parameters, a new approach has been proposed for studying the integral funnel (antifunnel) of a family of their solutions. Efficient conditions for a family of solutions to remain in an integral funnel (antifunnel) and conditions for narrowing of the integral funnel were established. The proposed approach is based on a comparison scheme and a set of regularized differential equations. The obtained results contribute to the development of the qualitative theory of uncertain systems and to the expansions of the appropriate applications.
- scalar nonlinear equation,
- uncertain parameters,
- nonporous fence,
- funnel,
- antifunnel
Citation: Anatoliy Martynyuk, Ivanka Stamova, Yulya Martynyuk–Chernienko. Estimation of the integral funnel for solutions of equations of perturbed motion with uncertain parameters[J]. AIMS Mathematics, 2025, 10(9): 21581-21594. doi: 10.3934/math.2025959

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Abstract

In this article, for scalar nonlinear equations with uncertain parameters, a new approach has been proposed for studying the integral funnel (antifunnel) of a family of their solutions. Efficient conditions for a family of solutions to remain in an integral funnel (antifunnel) and conditions for narrowing of the integral funnel were established. The proposed approach is based on a comparison scheme and a set of regularized differential equations. The obtained results contribute to the development of the qualitative theory of uncertain systems and to the expansions of the appropriate applications.

References

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