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Existence Results for Second-Order Nonlinear Differential Inclusion with Nonlocal Boundary Conditions

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Abstract

In this paper, we investigate the existence of solutions for a second-order differential inclusion with nonlocal boundary conditions. To establish the existence results for the given problem, first, we apply Schaefer’s fixed point theorem combined with a selection theorem of Bressan and Colombo. Secondly, our result is based on the Covitz–Nadler fixed point theorem for multivalued maps. An example is given to illustrate the obtained results.

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Authors and Affiliations

  1. Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO), University of Oran1, Ahmed Benbella, Algeria

    N. Bouteraa & S. Benaicha

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  1. N. Bouteraa
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  2. S. Benaicha
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Correspondence to N. Bouteraa or S. Benaicha.

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Translated from Sibirskii Zhurnal Vychislitel’noi Matematiki, 2021, Vol. 24, No. 1, pp. 35-45 https://doi.org/10.15372/SJNM20210103.

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Bouteraa, N., Benaicha, S. Existence Results for Second-Order Nonlinear Differential Inclusion with Nonlocal Boundary Conditions. Numer. Analys. Appl. 14, 30–39 (2021). https://doi.org/10.1134/S1995423921010031

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  • DOI: https://doi.org/10.1134/S1995423921010031

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