Malkhaz Ashordia
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