×

On the solvability of singular differential delay systems with variable coefficients. (English) Zbl 1167.34369

From the introduction: We consider singular differential delay systems with variable coefficients
\[ \begin{cases} E(t)\dot x(t) = A(t)x(t) + B(t)x(t - \tau) + f(t),\quad & t_0\geq t<t_1,\\ x(t) =\varphi(t), & t_0 -\tau\leq t\leq t_0,\end{cases}\tag{1} \]
in the interval \([t_0,t_1]\subset \mathbb R\). Here, \(x(t)\in C^n\) is a state vector, \(E(t)\), \(A(t)\in C([t_0,t_1],C^{m,n})\), \(B(t)\in C([t_0-\tau,t_1]\), \(C^{m,n})\), \(f(t)\in C([t_0,t_1],C^m)\), and \(\tau > 0\) is time delay, \(\varphi(t)\) is an initial function.
We give canonical forms of singular differential delay systems with variable coefficients, and finally, we study the solvability of the singular differential delay systems with variable coefficients.

MSC:

34K05 General theory of functional-differential equations
34K06 Linear functional-differential equations
PDFBibTeX XMLCite
Full Text: DOI