×

On a two point linear boundary value problem for system of ODEs with deviating arguments. (English) Zbl 1087.34044

In the paper, the general effective criterion for the unique solvability (in terms of C. Carathéodory) of two–point boundary value problem for a system of linear ordinary differential equations with deviating arguments of the form \[ \begin{aligned} x'(t) &= A (t) x (\tau _{11} (t)) + B (t) u (\tau _{12} (t)) + q_1(t), \quad t \in [0,T]\\ u'(t) &= C (t) x (\tau _{21} (t)) + D (t) u (\tau _{22} (t)) + q_2(t), \quad t \in [0,T]\\ \alpha _{11} x (0) &+ \alpha _{12} u (0) = c_0, \quad \alpha _{21} x (T) + \alpha _{22} u (T) = c_T \end{aligned} \] is established. Hence, the consequences for the system with a small parameter and for the system with constant delays are derived.

MSC:

34K10 Boundary value problems for functional-differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
PDFBibTeX XMLCite
Full Text: EuDML EMIS