Malkhaz Ashordia

On Two-Point Singular Boundary Value Problems for Systems of Linear Generalized Ordinary Differential Equations

abstract:
The two-point boundary value problem is considered for the system of linear generalized ordinary differential equations with singularities on a non-closed interval. The constant term of the system is a vector-function with bounded total variations components on the closure of the interval, and the components of the matrix-function have bounded total variations on every closed interval from this interval.
The general sufficient conditions are established for the unique solvability of this problem in the case where the system has singularities. Singularity is understand in a sense the components of the matrix-function corresponding to the system may have unbounded variations on the interval.
Relying on these results the effective conditions are established for the unique solvability of the problem.

Mathematics Subject Classification: 34K06, 34K10

Key words and phrases: Systems of linear generalized ordinary differential equations, singularity, the Lebesgue-Stiltjes integral, two-point boundary value problem