ASYMPTOTIC SOLUTIONS TO INITIAL VALUE PROBLEMS FOR SINGULARLY PERTURBED QUASI-LINEAR IMPULSIVE SYSTEMS

Abstract

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.