Systems of singular differential equations with pulse action

Advances in Difference Equations

Alexandr Boichuk¹  Martina Langerov³  Miroslava Rikov⁴  Evgenij Voitushenko⁵ 

[1] National Academy of Science of Ukraine, Kiev, Ukraine;Taras Shevchenko National University of Kiev, Kiev, Ukraine;University of Žilina, Žilina, Slovakia

关键词: singular systems;    impulsive action;    central canonical form;    existence of solutions;    Moore-Penrose pseudo-inverse matrix;   

DOI  :  10.1186/1687-1847-2013-186

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY