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Existence-uniqueness and fixed-point iterative method for general nonlinear fourth-order boundary value problems

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Abstract

Existence and uniqueness results are established for the general nonlinear fourth-order two-point boundary value problem with general linear homogeneous boundary conditions. The proofs are based on the Banach fixed-point theorem under the conditions that the nonlinear term is bounded and Lipschitz in a specific region. A fixed-point iterative method for finding the solution of the problem is also proposed with error estimates. The resulting iterative solutions automatically satisfy the boundary conditions provided that the initial iterate does so. Two examples are given to illustrate the applicability of the proposed approach and the efficiency of the iterative method.

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Acknowledgements

This work was supported by the Ministry of Science and Technology, Taiwan, R.O.C under Grant No. MOST 109-2221-E-269 -003.

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  1. Department of Mechanical Engineering, Far East University, Tainan, 74448, Taiwan, Republic of China

    Shih-Hsiang Chang

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  1. Shih-Hsiang Chang
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Correspondence to Shih-Hsiang Chang.

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Chang, SH. Existence-uniqueness and fixed-point iterative method for general nonlinear fourth-order boundary value problems. J. Appl. Math. Comput. 67, 221–231 (2021). https://doi.org/10.1007/s12190-020-01496-4

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  • DOI: https://doi.org/10.1007/s12190-020-01496-4

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