About the existence and uniqueness of solutions for some second-order nonlinear BVPs

Abstract

[EN] The significance of our work is to solve some second-order nonlinear boundary value prob-lems. To do this, we take into account the equivalence of the problems considered with certain integral equations, we will obtain a fixed-point-type result for these integral equa-tions. This result provides us the existence and uniqueness of solutions for the second -order nonlinear boundary value problems considered. As a novelty, we will use for this fixed-point-type result a family of third order iterative processes to approximate the so-lution, instead of the usually considered method of Successive Approximations of linear convergence. & COPY; 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )