Remarks and improvement regarding the theorem of continuous dependence of solutions of F.D.E., using some new results for continuous convergences

2017/03/29 by E.S. Athanasiadou, Athanasiadou, E., Christos Papachristodoulos +1
Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1703.10014

openalex publication_date 2017/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We improve the theorem on continuous dependence of solutions of functional differential equations (see J. Hale, Functional differential equations, theorem 5.1), using some new results on continuous convergences. Namely, we prove this theorem without the assumption of uniform boundeness for the sequence (f_k). Also we restore some inconsistencies regarding the proof of this theorem.

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