Abstract
Abstract The paper deals with the singular systems of ordinary differential equations with impulsive action under the assumption that the considered systems can be reduced into the central canonical form. An approach which combines the theory of impulsive differential equations and known results from the theory of singular Fredholm boundary value problems is used. Necessary and sufficient conditions for the existence of solutions of the singular boundary value problems with impulsive action are derived. Moreover, an algorithm for the construction of the family of linearly independent solutions is shown. MSC:34A09, 34A37.
Highlights
1 Introduction It is known that some of the problems of the control theory, radio physics, mathematical economics, linear programming and others can be modeled by systems of differential equations with a singular matrix
The origin of the theory of differential systems with impulsive action can be found in the work by Myshkis and Samoilenko [ ], later in the work by Samoilenko and Perestyuk [ ]
Let us consider the problem of existence and construction of solutions of the singular linear systems of ordinary differential equations with impulsive action at fixed points of time
Summary
It is known that some of the problems of the control theory, radio physics, mathematical economics, linear programming and others can be modeled by systems of differential equations with a singular matrix. Let us consider the problem of existence and construction of solutions of the singular linear systems of ordinary differential equations with impulsive action at fixed points of time
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