ASYMPTOTIC SOLUTIONS TO INITIAL VALUE PROBLEMS FOR SINGULARLY PERTURBED QUASI-LINEAR IMPULSIVE SYSTEMS
Aviltay N. Uaissov A.B.
30 September 2025al-Farabi Kazakh State National University
KazNU Bulletin. Mathematics, Mechanics, Computer Science Series
2025#127Issue 344 - 65 pp.
This paper investigates a singularly perturbed quasi-linear impulsive differential system with singularities present both in the differential equations and in the impulse functions. The boundary function method is employed to derive the main results. A uniform asymptotic approximation with higher accuracy is constructed and a complete asymptotic expansion is obtained. Theoretical findings are supported by illustrative examples and numerical simulations. The analysis reveals the presence of boundary and interior layers caused by the singular perturbation and impulsive effects. Sufficient conditions for the existence and uniqueness of the solution are established. The results contribute to the theoretical understanding of impulsive systems with complex singular structures and may be applicable to various problems in applied mathematics.
impulsive differential equations with singularities , singularly perturbed systems , small parameter , the boundary function method
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Al-Farabi Kazakh national university, Almaty, Kazakhstan
Al-Farabi Kazakh national university
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