Periodic problem for an impulsive system of the loaded hyperbolic equations

• Main Authors: Anar T. Assanova, Zhazira M. Kadirbayeva
• Format: Article
• Language: English
• Published: Texas State University 2018-03-01
• Series: Electronic Journal of Differential Equations
• Subjects: System of loaded hyperbolic equations; periodic problem; impulse effects; solvability
• Online Access: http://ejde.math.txstate.edu/Volumes/2018/72/abstr.html

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.