Title: First-order nonlinear dynamic initial value problems

Authors: Martin Bohner; Sanket Tikare; Iguer Luis Domini Dos Santos

Addresses: Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409-0020, USA ' Department of Mathematics, Ramniranjan Jhunjhunwala College, Ghatkopar (W), Mumbai (M.S.) – 400 086, India ' Faculdade de Engenharia de Ilha Solteira, Departamento de Matemática, UNESP – Universidade Estadual Paulista, Av. Brasil, 56, Ilha Solteira 15385-000, SP, Brazil

Abstract: We prove three existence theorems for solutions of first-order dynamic initial value problems, including corresponding continuous and discrete cases. The main tools are fixed point theorems and dynamic inequalities. Two more results are given that discuss dependence of solutions on the initial conditions as well as convergence of sequences of solutions.

Keywords: time scales; dynamic equation; first-order nonlinear; existence; continuous dependence; fixed point theorems; dynamic inequalities.

DOI: 10.1504/IJDSDE.2021.117358

International Journal of Dynamical Systems and Differential Equations, 2021 Vol.11 No.3/4, pp.241 - 254

Received: 22 Jun 2020
Accepted: 03 Oct 2020
Published online: 01 Sep 2021 *

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