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On higher-order nonlinear boundary value problems with nonlocal multipoint integral boundary conditions

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Abstract

In this paper, we study the existence of solutions for nonlinear nth-order ordinary differential equations and inclusions with nonlocal multipoint integral boundary conditions. Fixed point theorems due to Schaefer and Banach are employed to prove the existence results for the single-valued case, whereas the existence of solutions for the multivalued problem is established by means of a nonlinear alternative for Kakutani maps and Covitz–Nadler fixed point theorem. The obtained results are well explained by examples. We extend our discussion to some new problems.

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Authors and Affiliations

  1. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Bashir Ahmad, Ahmed Alsaedi & Nada Al-Malki

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  1. Bashir Ahmad
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  2. Ahmed Alsaedi
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  3. Nada Al-Malki
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Correspondence to Bashir Ahmad.

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Ahmad, B., Alsaedi, A. & Al-Malki, N. On higher-order nonlinear boundary value problems with nonlocal multipoint integral boundary conditions. Lith Math J 56, 143–163 (2016). https://doi.org/10.1007/s10986-016-9311-6

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  • DOI: https://doi.org/10.1007/s10986-016-9311-6

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