CMMSE: Solving Impulsive Boundary Value Problem for Nonlinear Differential Equations With Parameter
Temesheva S. Assanova A. Kadirbayeva Z.
15 March 2026John Wiley and Sons Ltd
Mathematical Methods in the Applied Sciences
2026#49Issue 42443 - 2455 pp.
This paper is devoted to the study of a two-point impulsive boundary value problem for a system of nonlinear first-order ordinary differential equations involving an unknown parameter appearing in both the differential equation and the boundary condition. The main objective is to establish sufficient conditions for the existence of an isolated solution within some set. To achieve this, we apply the Dzhumabaev parametrization method. Based on this approach, we develop a constructive algorithm for finding the solution. The method effectively addresses the discontinuities introduced by the impulses and ensures solvability under clearly defined conditions. A numerical example is presented to illustrate the efficiency and practical applicability of the proposed algorithm. The results demonstrate the methods potential for solving a wide range of nonlinear impulsive boundary value problems with parameters.
boundary condition with parameter , convergence , Dzhumabaev parameterization method , impulsive boundary value problem , isolated solution , nonlinear first-order differential equation with parameter , solvability conditions
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Al-Farabi Kazakh National University, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Kazakh National Womens Teacher Training University, Almaty, Kazakhstan
International Information Technology University, Almaty, Kazakhstan
Al-Farabi Kazakh National University
Institute of Mathematics and Mathematical Modeling
Kazakh National Womens Teacher Training University
International Information Technology University
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