OPERATOR THEORETIC TECHNIQUES IN THE THEORY OF NONLINEAR ORDINARY HYBRID DIFFERENTIAL EQUATIONS WITH MAXIMA

Abstract

In this paper the author proves the algorithms for the existence as well as approximations of the solutions for initial value problems of nonlinear $p^{th}$ order ordinary differential equations using the operator theoretic techniques in a partially ordered space. The main results rely on a recent hybrid fixed point theorems of Dhage (2013) in a partially ordered normed linear space ??and the approximations of the solutions of the considered nonlinear differential equations are obtained under weaker mixed continuity and Lipschitz conditions. Our hypotheses and results are also illustrated by some numerical examples.