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

Abstract

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.

Keywords

• mixed-type functional differential equation
• delayed argument
• advanced argument
• semi-global solution
• global solution
• monotone iterative method
• fixed-point theorem
• primary: 34k07; 34k25
• secondary: 34k60