Iterative methods for solutions of impulsive functional differential systems

Abstract

This paper presents iterative methods for impulsive functional differential systems. The basic idea of the iterative method is the monotone approach which involves the notions of upper and lower solutions and the construction of monotone sequences. By developing some comparison results for impulsive differential inequalities, we prove the existence of extremal solutions of the impulsive functional system in a sector, which can be obtained by iteration. When the solution of the system is unique, this approach provides numerical procedures for computation of solutions.

Keywords:

• Iterative method
• impulsive functional differential systems
• nonlinear
• comparison
• inequality

AMS:

• 34K05
• 65Q05