Lower and upper estimates of semi-global and global solutions to mixed-type functional differential equations

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In the paper, nonlinear systems of mixed-type functional differential equations are analyzed and the existence of semi-global and global solutions is proved. In proofs, the monotone iterative technique and Schauder-Tychonov fixed-point theorem are used. In addition to proving the existence of global solutions, estimates of their co-ordinates are derived as well. Linear variants of results are considered and the results are illustrated by selected examples.

Klíčová slova
Mixed-type functional differential equation
delayed argument
advanced argument
semi-global solution
Global solution
monotone iterative method
fixed-point theorem