Sharper existence and uniqueness results for solutions to third-order boundary value problems

    Saleh S. Almuthaybiri   Affiliation
    ; Christopher C. Tisdell   Affiliation


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.

Keyword : third-order boundary value problem, existence and uniqueness of solutions, Rus’s contraction mapping theorem, two metrics, three-point boundary conditions, sharp estimates

How to Cite
Almuthaybiri, S. S., & Tisdell, C. C. (2020). Sharper existence and uniqueness results for solutions to third-order boundary value problems. Mathematical Modelling and Analysis, 25(3), 409-420.
Published in Issue
May 13, 2020
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