The method of averaging is applied to study the existence solutions boundary value problems for systems differential equations with non-fixed moments impulse action. It shown that if an averaged problem has a solution, then original solvable as well. Here impulsive system simpler ordinary equations.

Antiperiodic problems arise naturally from the mathematical models of various of physical processes see 1, 2 , and also appear in the study of partial differential equations and abstract differential equations see 3–5 . For instance, electron beam focusing system in travelling-wave tube’s theories is an antiperiodic problem see 6 . During the past twenty years, antiperiodic problems have been s...

The theory of the nonlocal linear boundary value problems is still on the level of examples. Any attempt to encompass them by a unified scheme sticks upon the lack of general methods. Here we are to outline an algebraic approach to linear nonlocal boundary value problems. It is based on the notion of convolution of linear operator and on operational calculus on it. Our operators are right inver...

Abstract This paper is concerned with a class of boundary value problems for the nonlinear impulsive functional integro-differential equations with a parameter by establishing new comparison principles and using the method of upper and lower solutions together with monotone iterative technique. Sufficient conditions are established for the existence of extremal system of solutions for the given...