Ulam-Hyers stability of dynamic equations on time scales via Picard operators

作者：Andras Szilard^*; Meszaros Alpar Richard

来源：Applied Mathematics and Computation, 2013, 219(9): 4853-4864.

DOI：10.1016/j.amc.2012.10.115

• Ulam-Hyers
• Stability
• Picard operators
• Time scales
• Differential equations
• Integral equations

In this paper we study the Ulam-Hyers stability of some linear and nonlinear dynamic equations and integral equations on time scales. We use both direct and operatorial methods and we propose a unified approach to Ulam-Hyers stability based on the theory of Picard operators (see [28,33]). Our results extend some recent results from [24,25,8,14,13,5,6] to dynamic equations and are more general than the results from [1]. The operatorial point of view, based on the theory of Picard operators, allows to discuss the Ulam-Hyers stability of many types of differential- and integral equations on time scales and also to obtain simple and structured proofs to the existing results, but as we point out at our final remarks there are also a few disadvantages.

• 出版日期2013-1-1