SHARPER EXISTENCE AND UNIQUENESS RESULTS FOR SOLUTIONS TO THIRD-ORDER BOUNDARY VALUE PROBLEMS-Reference-Cited by-同舟云学术

SHARPER EXISTENCE AND UNIQUENESS RESULTS FOR SOLUTIONS TO THIRD-ORDER BOUNDARY VALUE PROBLEMS

Published:2020-05-13 Issue:3 Volume:25 Page:409-420
ISSN:1392-6292
Container-title:Mathematical Modelling and Analysis
language:
Short-container-title:

Author:

Almuthaybiri Saleh S.¹^ORCID,Tisdell Christopher C.²^ORCID

Affiliation:

1. School of Mathematics and Statistics, The University of New South Wales, UNSW, 2052 Sydney, Australia; Department of Mathematics, College of Sciences and Arts, Qassim University, Qassim, Oqlatu’s Soqoor, Saudi Arabia

2. School of Mathematics and Statistics, The University of New South Wales, UNSW, 2052 Sydney, Australia

Abstract

The purpose of this note is to sharpen Smirnov’s recent work on existence and uniqueness of solutions to third-order ordinary differential equations that are subjected to two- and three-point boundary conditions. The advancement is achieved in the following ways. Firstly, we provide sharp and sharpened estimates for integrals regarding various Green’s functions. Secondly, we apply these sharper estimates to problems in conjunction with Banach’s fixed point theorem. Thirdly, we apply Rus’s contraction mapping theorem in a metric space, where two metrics are employed. Our new results improve those of Smirnov by showing that a larger class of boundary value problems admit a unique solution.

Publisher

Vilnius Gediminas Technical University

Subject

Modeling and Simulation,Analysis

Reference10 articles.

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