Method for solving the periodic problem for an impulsive system of hyperbolic integro-differential equations

A. T. Assanova, E. А. Bakirova, Zh. М. Каdirbayeva

2017

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DOI 10.1063/1.5000620
Data confidence 70 medium
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Abstract

The periodic problem for a system of integro-differential equations of hyperbolic type with impulse effects is considered. This problem is reduced to an equivalent problem, consisting of a family of periodic boundary value problems for system of ordinary differential equations with parameter and impulse effects and integral relations by method of introducing additional functions. Sufficient conditions for existence of unique solution to the family of periodic boundary value problem with the impulse effects for system of the ordinary differential equations are received by parametrization method. Conditions for the unique solvability of periodic problem for system of integro - differential equations of hyperbolic type with impulse effects are established in the term of initial data.