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Principal eigenvalues and eigenfunctions to Lane-Emden systems on general bounded domains

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Abstract

We prove the existence of at least a curve of principal eigenvalues for two-parameter Lane-Emden systems under Dirichlet boundary conditions for general bounded domains. The nonhomogeneous counterpart is also addressed. Part of the main results (Theorems 1.1–1.3) are based on some deep ideas introduced in the seminal paper [4] and on two fundamental tools, both new and of independent interest: Aleksandrov–Bakelman–Pucci estimates (Theorem 2.1) and Harnack–Krylov–Safonov inequalities (Theorem 5.1) associated to Lane–Emden systems in smooth domains.

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Acknowledgments

The first author was partially supported by CNPq/Brazil (PQ 316526/2021-5) and Fapemig/Brazil (Universal-APQ-00709-18) and the second author was partially supported by CNPq/Brazil (PQ 302670/2019-0, Universal 429870/2018-3) and Fapemig/Brazil (PPM-00561-18).

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Authors and Affiliations

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

    Edir Junior Ferreira Leite

  2. Departamento de Matemática, Universidade Federal de Minas Gerais, Caixa Postal 702, 30123-970, Belo Horizonte, MG, Brazil

    Marcos Montenegro

Authors
  1. Edir Junior Ferreira Leite
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  2. Marcos Montenegro
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Correspondence to Marcos Montenegro.

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Leite, E.J.F., Montenegro, M. Principal eigenvalues and eigenfunctions to Lane-Emden systems on general bounded domains. Isr. J. Math. 259, 277–310 (2024). https://doi.org/10.1007/s11856-023-2487-7

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  • DOI: https://doi.org/10.1007/s11856-023-2487-7

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