Bounded solutions of dynamic equations on combined time scales

Year, pages: 2007, 273 - 281

In this paper we discuss asymptotic behavior of solutions of a dynamic equation

$$ u^Δ(t)=f(t,u(t)), $$

where $f:mathbb{T}×mathbb{R} ightarrowmathbb{R}$ and $mathbb{T}$ is a combined time scale with zero and nonzero graininess function. 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.

Václavíková, B. 2007. Bounded solutions of dynamic equations on combined time scales. In Tatra Mountains Mathematical Publications, vol. 38, no.4, pp. 273-281. 1210-3195.

Václavíková, B. (2007). Bounded solutions of dynamic equations on combined time scales. Tatra Mountains Mathematical Publications, 38(4), 273-281. 1210-3195.