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Eigenvalues of Elliptic Functional Differential Systems via a Birkhoff–Kellogg Type Theorem

Author

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  • Gennaro Infante

    (Dipartimento di Matematica e Informatica, Università della Calabria, Arcavacata di Rende, 87036 Cosenza, Italy)

Abstract

Motivated by recent interest on Kirchhoff-type equations, in this short note we utilize a classical, yet very powerful, tool of nonlinear functional analysis in order to investigate the existence of positive eigenvalues of systems of elliptic functional differential equations subject to functional boundary conditions. We obtain a localization of the corresponding non-negative eigenfunctions in terms of their norm. Under additional growth conditions, we also prove the existence of an unbounded set of eigenfunctions for these systems. The class of equations that we study is fairly general and our approach covers some systems of nonlocal elliptic differential equations subject to nonlocal boundary conditions. An example is presented to illustrate the theory.

Suggested Citation

  • Gennaro Infante, 2020. "Eigenvalues of Elliptic Functional Differential Systems via a Birkhoff–Kellogg Type Theorem," Mathematics, MDPI, vol. 9(1), pages 1-8, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2020:i:1:p:4-:d:466241
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    Cited by:

    1. Stefano Biagi & Alessandro Calamai & Gennaro Infante, 2023. "Nonzero positive solutions of fractional Laplacian systems with functional terms," Mathematische Nachrichten, Wiley Blackwell, vol. 296(1), pages 102-121, January.

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