Representation of solutions of difference equations with continuous time

H. Péics, University of Novi Sad, Subotica, Serbia and Montenegro

E. J. Qualitative Theory of Diff. Equ., Proc. 6'th Coll. Qualitative Theory of Diff. Equ., No. 21. (2000), pp. 1-8.

Abstract: This paper describes a representation of solutions of the system of nonautonomous functional equations $x(t)=A(t)x(t-1)+B(t)x(p(t))$, in form of series, using the Cauchy matrix of the linear system $y(t)=A(t)y(t-1)$. A representation of analitical solutions of the equation $x(t)=ax(t-1)+bx(pt)$ with constant coefficients is also investigated.

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