Department of Applied Mathematics, Faculty of Science, Žilina University, Hurbanova 15, 010 26 Žilina, Slovak Republic
AMS subject classification: 39A10, 39A11.
In this paper we discuss the asymptotic behavior of solutions of a dynamic equation where f: 핋 × ℝ → ℝ and 핋 is a time scale. We formulate a principle which gives the guarantee that the graph of at least one solution of above mentioned equation stays in the prescribed domain. This principle uses the idea of the retraction method and is a suitable tool for investigating the asymptotic behavior of solutions of dynamic equations. This is illustrated by an example.
Time scale, asymptotic behavior of solution, retract, retraction
