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Existence and Uniqueness of Solutions for a Third‐Order Three‐Point Boundary Value Problem via Measure of Noncompactness

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  • Chen Yang

Abstract

In this paper, we consider a nonlinear third‐order three‐point boundary value problem and give the existence and uniqueness of solutions by constructing Green’s function and using its properties. The methods used here are based on Darbo’s fixed point theorem combined with the technique of measure of noncompactness. Finally, as applications, two examples are given to illustrate our main results.

Suggested Citation

  • Chen Yang, 2022. "Existence and Uniqueness of Solutions for a Third‐Order Three‐Point Boundary Value Problem via Measure of Noncompactness," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:1157154
    DOI: 10.1155/2022/1157154
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    References listed on IDEAS

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    1. Zengji Du & Bensheng Zhao & Zhanbing Bai, 2014. "Solvability of a Third-Order Multipoint Boundary Value Problem at Resonance," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, February.
    2. Rabbani, Mohsen & Arab, Reza & Hazarika, Bipan, 2019. "Solvability of nonlinear quadratic integral equation by using simulation type condensing operator and measure of noncompactness," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 102-117.
    3. Zengji Du & Bensheng Zhao & Zhanbing Bai, 2014. "Solvability of a Third‐Order Multipoint Boundary Value Problem at Resonance," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Rabbani, Mohsen & Das, Anupam & Hazarika, Bipan & Arab, Reza, 2020. "Measure of noncompactness of a new space of tempered sequences and its application on fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Bashir Ahmad & Ahmed Alsaedi & Sotiris K. Ntouyas & Jessada Tariboon, 2017. "Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities," Springer Books, Springer, number 978-3-319-52141-1, January.
    6. Józef Banaś & Mohammad Mursaleen, 2014. "Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations," Springer Books, Springer, edition 127, number 978-81-322-1886-9, January.
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