Nonlinear Problem for a System of Two Impulse Systems of Equations with a Nonlinear Function under the Differential Sign and with a Product of Two Nonlinear Functions
Annotatsiya
In this article, nonlocal two-point boundary value problem for a system of two impulse systems of differential equations with a nonlinear function under the differential sign and with maxima is investigated. Each system of differential equations contains a product of two nonlinear vector functions, for each of which the Lipschitz condition is satisfied. The existence, uniqueness and continuous dependence of the solution on the given functions are proved. The problem is reduced 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 applied in proving the existence and uniqueness of a solution to nonlinear systems of functional integral equations with maxima.