Existence Results for Fuzzy Differential Equations via Truncation Operators Between an Upper and a Lower Solution and Fixed Point Results

In this work, we analyze the existence of solution to a fuzzy differential equation of first order in the fuzzy functional interval determined by an upper and a lower solution. The approach followed consists in the study of an auxiliary problem that is defined through a proper 'truncation operator' based on the choice of well ordered upper and lower solutions to the problem of interest. To our purpose, we justify that the truncation operator is well defined and satisfies some monotonicity properties. Finally, using the lattice structure of some subsets of the space of continuous fuzzy-valued functions and imposing some restrictions on the nonlinearity, we conclude the existence of solution to the equation on the interval [0,+infinity) by the application of Tarski's fixed point theorem.