First-order nonlinear dynamic initial value problems - Bohner, Martin; Tikare, Sanket; dos Santos, Iguer Luis Domini [UNESP] (Inderscience Publishers, 2021)
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: Continuous dependence; Dynamic equation; Dynamic inequalities; Existence; First-order nonlinear; Fixed point theorems; Time scales