Global solutions to nonlinear second order interval integrodifferential equations by fixed point in partially ordered sets

Abstract

In this paper, we prove the existence and uniqueness of global solution for second order interval valued integrodifferential equation with initial conditions admitting only the existence of a lower solution or an upper solution. In this study, in order to make the global solution on entire $[0,b]$, we use a fixed point in partially ordered sets on the subintervals of $[0,b]$ and obtain local solutions. Also, under weak conditions we show being well-defined a special kind of  H-difference involved in this work. Moreover, we compare the results of existence and uniqueness under consideration of two kind of partial ordering on fuzzy numbers.