Существование периодических решений линейных систем дифференциальных уравнений второго порядка с импульсным воздействием

This paper considers the problem of finding necessary and sufficient conditions for the periodicity of solutions to second-order linear differential equation systems with impulsive effects. We investigate the case where the eigenvalues of the system matrix are real and distinct. The solution for such systems is explicitly constructed, and the necessary and sufficient conditions for the existence of both a unique periodic solution and a two-parameter family of periodic solutions are established. Finally, an illustrative example is provided, along with the plots of the integral curve and the corresponding solution trajectory of the system considered in the example