Malkhaz Ashordia, Nato Kharshiladze

On the Well-Posedness of the Weighted Cauchy Problem for Systems of Linear Impulsive Differential Equations with Singularities

abstract:
The weighted Cauchy problem is considered for systems of linear impulsive differential equations with singularities. The singularity is considered in the sense that the matrix-and vector-functions corresponding to the impulsive system are not, in general, integrable at the initial point. Sufficient conditions are established for so-called H-well-posedness of the problem.

Mathematics Subject Classification: 34A12, 34A30, 34A37, 34K26

Key words and phrases: Impulsive differential equation, linear system, singularity, the weighted Cauchy problem, H-well-posedness