On the Qualitative Properties of Solutions of Linear and Nonlinear Dynamic Equations on Time Scales

Abstract

It is well known that obtaining analytic solutions of differential and difference equations is almost difficult especially in the case of nonlinear equations. So, the need to the qualitative properties of solutions arised in the last four decades one of the important qualitative properties is the stability theory. The idea of the time scales appeared by Hilger [42], to unify the results for both differential and difference equations. Since then many contribution offered (see [42, 24]). Recently the stability theory of functional equations has been strongly developed. Very important contributions to this subject were brought by Ulam [112], Rassias [95], Hyers et al. [46], Jung [51], Guo et al. [36], Kolmanovski˘ı and Myshkis [62], and Radu [94]. Our results are connected with some recent papers of Castro and Ramos [30] and Jung [51] (where integral and differential equations are considered), BotaBoriceanu and Petru¸sel [26], and Petru et al. [89] (where the Ulam–Hyers stability for operatorial equations and inclusions are discussed).