On the existence and uniqueness of solutions to dynamic equations | Zendy

Başak Karpuz | Zendy

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On the existence and uniqueness of solutions to dynamic equations

Author(s) -

Başak Karpuz

Publication year - 2018

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1612-40

Subject(s) - mathematics , uniqueness , dynamic equation , initial value problem , simple (philosophy) , peano existence theorem , picard–lindelöf theorem , cauchy problem , peano axioms , mathematical analysis , pure mathematics , fixed point theorem , discrete mathematics , nonlinear system , danskin's theorem , philosophy , physics , epistemology , quantum mechanics

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.

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