On the existence and uniqueness of solutions to dynamic equations

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KARPUZ B.

TURKISH JOURNAL OF MATHEMATICS, vol.42, no.3, pp.1072-1089, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 3
  • Publication Date: 2018
  • Doi Number: 10.3906/mat-1612-40
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1072-1089
  • Keywords: Cauchy-Peano theorem, Picard-Lidelof theorem, dynamic equations, time scales, TIME SCALES
  • Dokuz Eylül University Affiliated: Yes

Abstract

In this paper, we prove the well-known Cauchy-Peano theorem for existence of solutions to dynamic equations on time scales. Some simple examples are given to show that there may exist more than a single solution for dynamic initial value problems. Under some certain conditions, it is also shown that there exists only one solution.