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Nonzero positive solutions of fractional Laplacian systems with functional terms

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  • Stefano Biagi
  • Alessandro Calamai
  • Gennaro Infante

Abstract

We study the existence of nonzero positive solutions of a class of systems of differential equations driven by fractional powers of the Laplacian. Our approach is based on the notion of fixed point index, and allows us to deal with nonlocal functional weights and functional boundary conditions. We present two examples to shed light on the type of functionals and growth conditions that can be considered with our approach.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:1:p:102-121
    DOI: 10.1002/mana.202100074
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    References listed on IDEAS

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    1. Gennaro Infante, 2020. "Eigenvalues of Elliptic Functional Differential Systems via a Birkhoff–Kellogg Type Theorem," Mathematics, MDPI, vol. 9(1), pages 1-8, December.
    2. Claudianor O. Alves & Romildo N. de Lima & Alânnio B. Nóbrega, 2018. "Bifurcation properties for a class of fractional Laplacian equations in RN," Mathematische Nachrichten, Wiley Blackwell, vol. 291(14-15), pages 2125-2144, October.
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