A retract principle on discrete time scales

• Autorzy: Diblik J. , Ruzickova M. , Vaclavikova B.
• Języki publikacji: EN

Abstrakty

EN

In this paper we discuss asymptotic behavior of solutions of a class of scalar discrete equations on discrete real time scales. A powerful tool for the investigation of various qualitative problems in the theory of ordinary differential equations as well as delayed differential equations is the retraction method. The development of this method is discussed in the case of the equation mentioned above. Conditions for the existence of a solution with its graph remaining in a predefined set are formulated. Examples are given to illustrate the results obtained.

Słowa kluczowe

EN

discrete equation; discrete time scale; asymptotic behavior of solution; retract; retraction

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2006
• Tom: Vol. 26, no. 3
• Strony: 445--455
• Opis fizyczny: Bibliogr. 8 poz., rys., wykr.

Twórcy

autor

Diblik J.

autor

Ruzickova M.

autor

Vaclavikova B.

• Zilina University, Department of Applied Mathematics, Faculty of Science, Hurbanova 15, 010 26 Zilina, Slovak Republic,

Bibliografia

• [1] M. Bohner, A. Peterson, Dynamic Equations on Time Scales, Birghauser, 2001.
• [2] K. Borsuk, Theory of Retracts, PWN, Warsaw, 1967.
• [3] J. Diblik, Asymptotic behavior of solutions of discrete equations, Funct. Differ. Equ. 11 (2004), 37-48.
• [4] J. Diblik, Anti-Lyapunov method for systems of discrete equations, Nonlinear Anal. 57 (2004), 1043-1057.
• [5] S. Hilger, Analysis on measure chains - a unified approach to continuous and discrete calculus, Results Math. 18 (1990), 18-56.
• [6] V. Lakshmikantham, S. Leela, Differential and Integral Inequalities, Vol. I - Ordinary Differential Equations, Academic Press, New York, London, 1969.
• [7] K.P. Rybakowski, Ważewski's principle for retarded functional differential equations, J. Diff. Equat. 36 (1980), 117-138.
• [8] T. Ważewski, Sur un principe topologique de l'examen de l’allure asymptotique des integrales des equations differentielles ordinaires, Ann. Soc. Polon. Math. 20 (1947), 279-313.