Линейные системы с вырожденным импульсным воздействием и сопряженные к ним

Abstract

Побудована система, спряжена до лiнiйної однорiдної системи з виродженим iмпульсним впливом. Знайдено умови iснування та побудови оператора Грiна цiєї задачi.

The existence conditions, dual system and generalized Green operator are obtained to construct the solutions of linear systems of ordinary differential equations with singular impulse action. This problem has some characteristic features by which it differs fundamentally from a similar problem with nonsingularly impulsively perturbed differential system. Above all it is the fact that not all solutions can be continued from left to right length of interval on which solutions of linear systems with singular impulse action exists.