Opuscula Math. 26, no. 3 (2006), 445-455

Opuscula Mathematica

A retract principle on discrete time scales

Josef Diblík
Miroslava Růžičková
Barbora Václavíková

Abstract. 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.

Keywords: discrete equation, discrete time scale, asymptotic behavior of solution, retract, retraction.

Mathematics Subject Classification: 39A10, 39A11.

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Cite this article as:
Josef Diblík, Miroslava Růžičková, Barbora Václavíková, A retract principle on discrete time scales, Opuscula Math. 26, no. 3 (2006), 445-455

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