Display Abstract

Title Regular variation on various time scales and its application to dynamic equations

Name Pavel \v Reh\'ak
Country Czech Rep
Email rehak@math.cas.cz
Co-Author(s)
Submit Time 2010-02-16 06:01:14
Session
Special Session 48: Differential, Difference, and Dynamic Equations
Contents
This is joint work with my Ph.D. student Ji\v r\'{\i} V\'{\i}tovec. We discuss the concept of regular and rapid variation on time scales. We show that parallel theories of regular and rapid variation on individual time scales may differ, and there is a need of certain additional conditions on the graininess $\mu$, which cannot be omitted. In particular, the cases where $\mu(t)=o(t)$ as $t\to\infty$ and $\mu(t)=(q-1)t$ with $q>1$ (i.e., $q$-calculus) are examined. The obtained theory is applied to study asymptotic behavior of solutions to second order dynamic equations.