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

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 introdu...

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Bibliographic Details
Published in:Israel journal of mathematics Vol. 259; no. 1; pp. 277 - 310
Main Authors: Leite, Edir Junior Ferreira, Montenegro, Marcos
Format: Journal Article
Language:English
Published: Jerusalem The Hebrew University Magnes Press 01.03.2024
Springer Nature B.V
Subjects:
Algebra
Analysis
Applications of Mathematics
Boundary conditions
Eigenvalues
Eigenvectors
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theorems
Theoretical
ISSN:0021-2172, 1565-8511
Online Access:Get full text
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Summary: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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ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-023-2487-7