Abstract
In this paper, the upper and lower solution method is proposed in order to solve the second order interval boundary value problem. We study first a class of linear interval boundary value problems and then investigate a class of nonlinear interval boundary value problems by the upper and lower solution method under the gH-derivative, and we prove that there exist at least two solutions.
Highlights
In 2018, by applying the monotone iterative technique, Hoa considered the extremal solutions to initial value problems of fractional interval-valued integro-differential equations [12]
We present the concept of upper and lower solution of a two-point boundary value problem of nonlinear interval differential equation under the gH-derivative in the following definition
By Theorem 4, we know that there exists V1 ( x ) ∈ C2 I, KC, which is the solution of the linear interval boundary value problem
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. In 2018, by applying the monotone iterative technique, Hoa considered the extremal solutions to initial value problems of fractional interval-valued integro-differential equations [12] These studies expanded the scope of the research on interval-valued differential equations. Rodríguez-López applied the upper and lower solution method to develop a monotone iterative technique to approximate extremal solutions for the initial value problem relative to a fuzzy differential equation in a fuzzy functional interval [14]. Motivated by this idea, in order to solve the nonlinear interval boundary value problem. We give a example to illustrate the effectiveness of the results in this paper
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