Jiří Šremr
abstract:
The presented work deals with the question on the existence and uniqueness of a
solution of the initial value problem for two-dimensional systems of linear
functional differential equations.
Unimprovable efficient conditions sufficient for the unique solvability of the
problem considered are established. The question on the existence of a
constant-sign solution is also studied in detail. In other words, theorems on
systems of linear functional differential inequalities (maximum principles) are
discussed, which play a crucial role not only in studies of solvability of
linear and non-linear problems but also for other topics related to the theory
of boundary value problems (e.g., oscillation theory, asymptotic theory, etc.).
The general results are applied to special cases of functional differential
systems, namely, to systems of differential equations with arguments deviations
and integro-differential systems, in which case further results are derived; the
criteria obtained contain results well-know for ordinary differential systems.
Mathematics Subject Classification: 34K06, 34K10
Key words and phrases: Two-dimensional linear functional differential system, initial value problem, unique solvability, system of differential inequalities