On the existence and uniqueness of solutions to dynamic equations

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KARPUZ B.

TURKISH JOURNAL OF MATHEMATICS, cilt.42, sa.3, ss.1072-1089, 2018 (SCI-Expanded, Scopus, TRDizin)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 3
  • Basım Tarihi: 2018
  • Doi Numarası: 10.3906/mat-1612-40
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1072-1089
  • Anahtar Kelimeler: Cauchy-Peano theorem, Picard-Lidelof theorem, dynamic equations, time scales
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

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.