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Principal curves to fractional m-Laplacian systems and related maximum and comparison principles

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Abstract

In this paper we develop a comprehensive study on principal eigenvalues and both the (weak and strong) maximum and comparison principles related to an important class of nonlinear systems involving fractional m-Laplacian operators. Explicit lower bounds for principal eigenvalues of this system in terms of the diameter of bounded domain \(\varOmega \subset {\mathbb {R}}^N\) are also proved. As application, we measure explicitly how small has to be \(\text {diam}(\varOmega )\) so that weak and strong maximum principles associated to this problem hold in \(\varOmega \).

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Acknowledgements

The first author was partially supported by FAPEMIG/ APQ-02375-21, APQ-04528-22, FAPEMIG/RED-00133-21 and CNPq Process 307575/2019-5. The second author was partially supported by CNPq/Brazil (PQ 316526/2021-5) and Fapemig/Brazil (Universal-APQ-00709-18). The authors are indebted to the anonymous referees for their careful reading and valuable comments in order to improve the work.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Viçosa, Viçosa, MG, 36570-900, Brazil

    Anderson L. A. de Araujo & Aldo H. S. Medeiros

  2. Departamento de Matemática, Universidade Federal de São Carlos, São Carlos, SP, 13565-905, Brazil

    Edir J. F. Leite

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  1. Anderson L. A. de Araujo
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  2. Edir J. F. Leite
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Correspondence to Edir J. F. Leite.

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de Araujo, A.L.A., Leite, E.J.F. & Medeiros, A.H.S. Principal curves to fractional m-Laplacian systems and related maximum and comparison principles. Fract Calc Appl Anal (2024). https://doi.org/10.1007/s13540-024-00293-1

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  • DOI: https://doi.org/10.1007/s13540-024-00293-1

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