On a (ω, c)−periodic solution for an impulsive system of second-order differential equation with product of two nonlinear functions and mixed maxima

Existence and uniqueness of (ω, c)−periodic solution of boundary value problem for an impulsive system of ordinary differential equations with a nonlinear function under the sign of the second-order differential, product of two nonlinear functions and mixed maxima are investigated. This problem is reduced to the investigation of (ω, c)−periodic solvability of the system of nonlinear functional-integral equations. The method of contracted mapping is used in the proof of unique solvability of nonlinear functional-integral equations in the space BD ([0, ω], Rn).