An explicit formula for solutions of some system of linear delay difference equations

• Autorzy: Kwapisz M. , Łachacz M.
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to provide an explicit formula for solutions of the following system of delay difference equations (wzór) where (wzór) ;αn= [n/k] (the symbol [x] stands for entire part of the real number x and k is a fixed positive integer). (An), (Bn), n∈ N, are sequences of square matrices of order m, (fn) is a sequence of vectors from Rm. From this formula conditions for the stability and asymptotic stability of solutions are derived.

Słowa kluczowe

EN

difference equations; asymptotic theory

PL

równania różnicowe; teoria asymptotyczna

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2002
• Tom: Vol. 8, nr 1
• Strony: 23--32
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Kwapisz M.

• Insitute of Mathematics Academy of Bydgoszcz Ul. Weyssenhoffa 11 85-072 Bydgoszcz, Poland

autor

Łachacz M.

• Insitute of Mathematics Academy of Bydgoszcz Ul. Weyssenhoffa 11 85-072 Bydgoszcz, Poland

Bibliografia

• [1] Agarwal, R. P., Difference Equations and Inequalities, Theory, Methods and Applications, Marcel Dekker, New York, 1992.
• [2] Elaydi, S. N., An Introduction to Difference Equations, Springer, Berlin, 1991.
• [3] Bartoszewski, Z., Kwapisz, M., An Introduction to Financial Mathematics (in Polish), Bydgoszcz Pedagogical University Publications, Bydgoszcz, 1998.
• [4] Gandolfo, G., Economic Dynamics, Springer, Berlin, 1980.
• [5] Lakshmikantham, V., Trigiante, D., Theory of Difference Equations: Numerical Methods and Applications, Academic Press, London, 1988.
• [6] Kwapisz, M., Elements of the Theory of Recurence Equations (in Polish), Gdansk University Publications, Gdansk, 1983.
• [7] Kwapisz, M., On difference equations arising in mathematics of finance, Nonlinear Anal. 30(2) (1997), 1207-1218.
• [8] Kwapisz, M., An explicit formula for solutions of some linear delay difference equation, Rocznik Naukowo-Dydaktyczny WSP-Krakow, (to appear).
• [9] Murata, Y., Mathematics for Stability and Optimization of Economic Systems, Academic Press, New York, 1977.
• [10] Nikaido, H Convex Struktures and Economic Theory, Academic Press, New York, 1968.