First-Order Nonlinear Dynamic Initial Value Problems
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.
M. Bohner et al., "First-Order Nonlinear Dynamic Initial Value Problems," International Journal of Dynamical Systems and Differential Equations, vol. 11, no. 3 thru 4, pp. 241 - 254, Inderscience, Sep 2021.
The definitive version is available at https://doi.org/10.1504/IJDSDE.2021.117358
Mathematics and Statistics
Keywords and Phrases
Continuous Dependence; Dynamic Equation; Dynamic Inequalities; Existence; First-Order Nonlinear; Fixed Point Theorems; Time Scales
International Standard Serial Number (ISSN)
Article - Journal
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01 Sep 2021