On a Nonlocal Problem for Nonlinear Impulse Systems of Second-Order Differential Equations with Nonlinea Boundary Conditions

A nonlocal two-point boundary value problem for impulsive systems of second-order ordinary differential equations with nonlinear conditions, including derivatives of an unknown vector function, is studied. The system of differential equations contains the product of two nonlinear vector functions, for each of them the Lipschitz condition is satisfied. The existence, uniqueness and continuous dependence of the solution from given functions are proved. The problem reduces to a system of nonlinear functional integral equations in a Banach space. The method of successive approximations in combination with the method of contraction mappings is used to prove the existence and uniqueness of solution to nonlinear systems of functional integral equations.