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Periodic problem for an impulsive system of the loaded hyperbolic equations. (English) Zbl 1398.35282

Summary: We consider a periodic problem for a system of the loaded hyperbolic equations with impulse effects. By introducing additional functions, this problem is reduced to an equivalent problem consisting of a family of periodic boundary-value problems of loaded ordinary differential equations with impulse effects and integral relations. We obtain sufficient conditions for the existence of unique solution to the family of periodic boundary-value problems. Conditions of unique solvability of periodic problem are established in terms of initial data.

MSC:

35R12 Impulsive partial differential equations
35B10 Periodic solutions to PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations
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