Vol. 9(1) Jan. 2021, No. 4, pp. 37-51.

DHAGE ITERATION METHOD FOR PBVPS OF NONLINEAR FIRST ORDER IMPULSIVE DIFFERENTIAL EQUATIONS
Vol. 9(1) Jan. 2021, No. 4, pp. 37-51
BAPURAO C. DHAGE

 

Abstract

In this paper we prove a couple of existence and approximation theorems for the PBVPs of first order nonlinear impulsive differential equations under certain mixed partial Lipschitz and partial compactness type conditions. Our main results are based on Dhage iteration method embodied in the hybrid fixed point principles of Dhage (2014) involving the sum of two monotone nondecreasing operators in a partially ordered Banach space. Our abstract main result is also illustrated by indicating a numerical example. We claim that the results of this paper are new and complement the work of Li et al [22] and Nieto [23, 24] on PBVPs of nonlinear impulsive differential equations


Full Text (PDF 366 K)