Jñānābha‎, Vol. 50 (1) (2020), 265-278

ITERATION PRINCIPLE FOR IVPS OF NONLINEAR FIRST ORDER IMPULSIVE DIFFERENTIAL EQUATIONS

By

Bapurao C. Dhage
“Kasubai”, Gurukul Colony, Thodga Road
Ahmedpur - 413515, Dist. Latur, Maharashtra, India.
Email:bcdhage@gmail.com
(Received : April 09, 2019 ; Revised: June 23, 2020)


Abstract

In this paper we prove the existence and approximation theorems for the initial value problems of first order nonlinear impulsive differential equations under certain mixed partial Lipschitz and partial compactness type conditions. Our results are based on the Dhage monotone iteration principle embodied in a hybrid fixed point theorem of Dhage involving the sum of two monotone order preserving operators in a partially ordered Banach space. The novelty of the present approach lies the fact that we obtain an algorithm for the solution. Our abstract main result is also illustrated by indicating a numerical example.

2010 Mathematics Subject Classifications: 47H07, 47H10, 34A12, 34A45
Keywords and phrases: Impulsive differential equation; Dhage iteration method; hybrid fixed point principle; existence and approximate solution.