Research Article
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Year 2025, Volume: 6 Issue: 2, 165 - 181, 30.07.2025

Döndü Öz

https://doi.org/10.54974/fcmathsci.1614200

Abstract

References

  • Abbas M., Zada A., Kallekhkim A., Switched impulsive integro-delay dynamic system and its controllability, Journal of Control and Decision, Published Online: 10 July 2025.
  • Akgöl S.D., Georgiev S.G., Kuş M.E., Existence of solutions for first order impulsive periodic boundary value problems on time scales, Filomat, 37(10), 3029-3042, 2023.
  • Almenar P., Jodar L., The principal eigenvalue of some nth order linear boundary value problems, Boundary Value Problems, 84, 16, 2021.
  • Bainov D.D., Simeonov P.S., Impulsive Differential Equations: Periodic Solutions and Applications of Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific Technical, 66, 1993.
  • Bainov D.D., Simeonov P.S., Systems with Impulse Effect, Stability Theory and Applications, Ellis Horwood, 1989.
  • Bi Z., Liu S., Positive solutions for third-order boundary value problems with indefinite weight, Mediterranean Journal of Mathematics, 20, 306, 2023.
  • Bouabdallah M., Chakrone O., Chehabi M., Eigenvalue problem of an impulsive differential equation governed by the one-dimensional p-Lap operator, Proyecciones Journal of Mathematics, 41(1), 217-247, 2022.
  • Canfield J., Galler A., Freericks J.K., The Laplace method for energy eigenvalue problems in quantum mechanics, Quantum Reports, 5(2), 370-397, 2023.
  • Eloe P.W., Neugebauer J.T., Smallest eigenvalues for boundary value problems of two term fractional differential operators depending on fractional boundary conditions, Electronic Journal of Differential Equations, 2021(62), 1-14, 2021.
  • Feliz M., Rui C., Third-order generalized discontinuous impulsive problems on the half-line, Mathematical Modelling and Analysis, 26(4), 548-565, 2021.
  • Georgiev S.G., Akgöl S.D., Kuş M.E., Existence of solutions for third order multi point impulsive boundary value problems on time scales, Miskolc Mathematical Notes, 23(2), 677-690, 2022.
  • Guo D., Lakshmikantham V., Nonlinear Problems in Abstract Cones, Academic Press, 1988.
  • Karaca I.Y., Fen F.T., Eigenvalues for iterative systems of dynamic equations with integral boundary conditions, Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 64(1), 87-97, 2015.
  • Lakshmikantham V., Bainov D.D., Simeonov P.S., Theory of Impulsive Differential Equations, World Scientific Publishing, Vol. 6 of Series in Modern Applied Mathematics, 1989.
  • Li J., Chen X., Eigenvalue-based stability analysis for impulsive control systems in robotics, Automatica, 158, 111256, 2023.
  • Mosazadeh S., Local stability of half inverse problems with boundary conditions dependent on the spectral parameter, Journal of Mathematical Analysis and Applications, 531(2), 12, 2024.
  • Nguyen T.H., Tran Q.V., Spectral methods for vibration analysis in impulsive mechanical systems, Journal of Sound and Vibration, 572, 118123, 2024.
  • Öz D., Karaca I.Y., Eigenvalue intervals for iterative systems of the second-order impulsive boundary value problem, Bulletin of the International Mathematical Virtual Institute, 12(2), 297-307, 2022.
  • Öz D., Karaca I.Y., Eigenvalue intervals for iterative systems of second-order nonlinear equations with impulses and m-point boundary conditions, Fixed Point Theory, 25(1), 289-307, 2024.
  • Öztürk S.N., Mukhtarov O., Aydemir K., Non-classical periodic boundary value problems with impulsive conditions, Journal of New Results in Science, 12(1), 1-8, 2023.
  • Prasad K.R., Sreedhar N., Srinivas M.A.S., Eigenvalue intervals for iterative systems of nonlinear three-point boundary value problems on time scales, Nonlinear Studies, 22(3), 419-431, 2015.
  • Prasad K.R., Bhushanam K., Countably many positive symmetric solutions for Sturm Liouville type boundary conditions of second-order iterative system, Creative Mathematics and Informatics, 33(2), 245-258, 2024.
  • Ramkumar K., Ravikumar K., Elsayed E.M., Existence and exponential stability of a class of impulsive neutral stochastic integrodifferential equations with Poisson jumps, Fundamentals of Contemporary Mathematical Sciences, 1(2), 71-83, 2020.
  • Rao S.N., Khuddush M., Ahmadini A.A.H., Existence of positive solutions for a nonlinear iterative system of boundary value problems with tempered fractional order derivative, Journal of Mathematics, 2024(1), 8862634, 18, 2024.
  • Shen L., Liu X., Lu Z., Multiplicity of positive solutions for four-point boundary value problems of impulsive differential equations with p-Laplacian, Electronic Journal of Differential Equations, 2010(52), 1-10, 2010.
  • Stamova I., Stamov G., Applied Impulsive Mathematical Models, CMS Books in Mathematics, Springer Cham, 2016.
  • Sun J., Qiao F., Wu Q., Impulsive control of a financial model, Physics Letters A, 335(4), 282-288, 2005.
  • Vatolkin M.Y., Investigation of the asymptotics of the eigenvalues of a second-order quasidifferential boundary value problem, Russian Mathematics, 68(3), 11-30, 2024.
  • Vatolkin M.Y., On the approximation of the first eigenvalue of some boundary value problems, Computational Mathematics and Mathematical Physics, 64(6), 1224-1239, 2024.
  • Yates J.R., Dissecting drug effects in preclinical models of impulsive choice: Emphasis on glutamatergic compounds, Psychopharmacology, 235(3), 607-626, 2018.
  • Zhang H., Yao W., Three solutions for a three-point boundary value problem with instantaneous and non-instantaneous impulses, AIMS Mathematics, 8(9), 21312-21328, 2023.
  • Zhang N., Ao J., Eigenvalues of some third-order boundary value problems with eigenparameter-dependent boundary conditions on time scales, Communications on Analysis and Computation, 3, 17-30, 2025.
  • Zhang Q., Tong P., Wu X., Liu J., Wan L., Leader-following impulsive consensus of third-order nonlinear multi-agent systems with delay, Physica A: Statistical Mechanics and its Applications, 672, 130661, 2025.
  • Zhao J., Yao G., Liu R., Zhu Y., Gao K., Wang M., Interval analysis of the eigenvalues of closed-loop control systems with uncertain parameters, 9(2), 31, 2020.

Some Results on Eigenvalue Intervals for Positive Solutions of the 3rd -order Impulsive Boundary Value Problem’s Iterative System with p-Laplacian Operator

Year 2025, Volume: 6 Issue: 2, 165 - 181, 30.07.2025

Döndü Öz

https://doi.org/10.54974/fcmathsci.1614200

Abstract

The objective of this paper is to determine the eigenvalue intervals for which positive solutions are guaranteed for the iterative system of the 3rd -order impulsive boundary value problem. The existence of solutions is established by applying the well-known Guo-Krasnosel’skii fixed point theorem. An illustrative example is provided to demonstrate the applicability of the theoretical results.

Keywords

Fixed point Impulsive BVP Iterative systems Eigenvalue interval

Ethical Statement

The author declares that the materials and methods used in her study do not require ethical committee and/or legal special permission.

References

  • Abbas M., Zada A., Kallekhkim A., Switched impulsive integro-delay dynamic system and its controllability, Journal of Control and Decision, Published Online: 10 July 2025.
  • Akgöl S.D., Georgiev S.G., Kuş M.E., Existence of solutions for first order impulsive periodic boundary value problems on time scales, Filomat, 37(10), 3029-3042, 2023.
  • Almenar P., Jodar L., The principal eigenvalue of some nth order linear boundary value problems, Boundary Value Problems, 84, 16, 2021.
  • Bainov D.D., Simeonov P.S., Impulsive Differential Equations: Periodic Solutions and Applications of Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific Technical, 66, 1993.
  • Bainov D.D., Simeonov P.S., Systems with Impulse Effect, Stability Theory and Applications, Ellis Horwood, 1989.
  • Bi Z., Liu S., Positive solutions for third-order boundary value problems with indefinite weight, Mediterranean Journal of Mathematics, 20, 306, 2023.
  • Bouabdallah M., Chakrone O., Chehabi M., Eigenvalue problem of an impulsive differential equation governed by the one-dimensional p-Lap operator, Proyecciones Journal of Mathematics, 41(1), 217-247, 2022.
  • Canfield J., Galler A., Freericks J.K., The Laplace method for energy eigenvalue problems in quantum mechanics, Quantum Reports, 5(2), 370-397, 2023.
  • Eloe P.W., Neugebauer J.T., Smallest eigenvalues for boundary value problems of two term fractional differential operators depending on fractional boundary conditions, Electronic Journal of Differential Equations, 2021(62), 1-14, 2021.
  • Feliz M., Rui C., Third-order generalized discontinuous impulsive problems on the half-line, Mathematical Modelling and Analysis, 26(4), 548-565, 2021.
  • Georgiev S.G., Akgöl S.D., Kuş M.E., Existence of solutions for third order multi point impulsive boundary value problems on time scales, Miskolc Mathematical Notes, 23(2), 677-690, 2022.
  • Guo D., Lakshmikantham V., Nonlinear Problems in Abstract Cones, Academic Press, 1988.
  • Karaca I.Y., Fen F.T., Eigenvalues for iterative systems of dynamic equations with integral boundary conditions, Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 64(1), 87-97, 2015.
  • Lakshmikantham V., Bainov D.D., Simeonov P.S., Theory of Impulsive Differential Equations, World Scientific Publishing, Vol. 6 of Series in Modern Applied Mathematics, 1989.
  • Li J., Chen X., Eigenvalue-based stability analysis for impulsive control systems in robotics, Automatica, 158, 111256, 2023.
  • Mosazadeh S., Local stability of half inverse problems with boundary conditions dependent on the spectral parameter, Journal of Mathematical Analysis and Applications, 531(2), 12, 2024.
  • Nguyen T.H., Tran Q.V., Spectral methods for vibration analysis in impulsive mechanical systems, Journal of Sound and Vibration, 572, 118123, 2024.
  • Öz D., Karaca I.Y., Eigenvalue intervals for iterative systems of the second-order impulsive boundary value problem, Bulletin of the International Mathematical Virtual Institute, 12(2), 297-307, 2022.
  • Öz D., Karaca I.Y., Eigenvalue intervals for iterative systems of second-order nonlinear equations with impulses and m-point boundary conditions, Fixed Point Theory, 25(1), 289-307, 2024.
  • Öztürk S.N., Mukhtarov O., Aydemir K., Non-classical periodic boundary value problems with impulsive conditions, Journal of New Results in Science, 12(1), 1-8, 2023.
  • Prasad K.R., Sreedhar N., Srinivas M.A.S., Eigenvalue intervals for iterative systems of nonlinear three-point boundary value problems on time scales, Nonlinear Studies, 22(3), 419-431, 2015.
  • Prasad K.R., Bhushanam K., Countably many positive symmetric solutions for Sturm Liouville type boundary conditions of second-order iterative system, Creative Mathematics and Informatics, 33(2), 245-258, 2024.
  • Ramkumar K., Ravikumar K., Elsayed E.M., Existence and exponential stability of a class of impulsive neutral stochastic integrodifferential equations with Poisson jumps, Fundamentals of Contemporary Mathematical Sciences, 1(2), 71-83, 2020.
  • Rao S.N., Khuddush M., Ahmadini A.A.H., Existence of positive solutions for a nonlinear iterative system of boundary value problems with tempered fractional order derivative, Journal of Mathematics, 2024(1), 8862634, 18, 2024.
  • Shen L., Liu X., Lu Z., Multiplicity of positive solutions for four-point boundary value problems of impulsive differential equations with p-Laplacian, Electronic Journal of Differential Equations, 2010(52), 1-10, 2010.
  • Stamova I., Stamov G., Applied Impulsive Mathematical Models, CMS Books in Mathematics, Springer Cham, 2016.
  • Sun J., Qiao F., Wu Q., Impulsive control of a financial model, Physics Letters A, 335(4), 282-288, 2005.
  • Vatolkin M.Y., Investigation of the asymptotics of the eigenvalues of a second-order quasidifferential boundary value problem, Russian Mathematics, 68(3), 11-30, 2024.
  • Vatolkin M.Y., On the approximation of the first eigenvalue of some boundary value problems, Computational Mathematics and Mathematical Physics, 64(6), 1224-1239, 2024.
  • Yates J.R., Dissecting drug effects in preclinical models of impulsive choice: Emphasis on glutamatergic compounds, Psychopharmacology, 235(3), 607-626, 2018.
  • Zhang H., Yao W., Three solutions for a three-point boundary value problem with instantaneous and non-instantaneous impulses, AIMS Mathematics, 8(9), 21312-21328, 2023.
  • Zhang N., Ao J., Eigenvalues of some third-order boundary value problems with eigenparameter-dependent boundary conditions on time scales, Communications on Analysis and Computation, 3, 17-30, 2025.
  • Zhang Q., Tong P., Wu X., Liu J., Wan L., Leader-following impulsive consensus of third-order nonlinear multi-agent systems with delay, Physica A: Statistical Mechanics and its Applications, 672, 130661, 2025.
  • Zhao J., Yao G., Liu R., Zhu Y., Gao K., Wang M., Interval analysis of the eigenvalues of closed-loop control systems with uncertain parameters, 9(2), 31, 2020.
There are 34 citations in total.

Details

Primary Language English
Subjects Ordinary Differential Equations, Difference Equations and Dynamical Systems
Journal Section Research Articles
Authors

Döndü Öz 0000-0001-9689-5475

Publication Date July 30, 2025
Submission Date January 6, 2025
Acceptance Date July 27, 2025
Published in Issue Year 2025 Volume: 6 Issue: 2

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