Generalizations and properties of the principal eigenvalue of elliptic\n operators in unbounded domains

2010/08/28 by Henri Berestycki, Luca Rossi, Berestycki, Henri +1 · 2 citations
Computer Science · Mathematics · #35B09 #35B50 #35J15 #35P15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1008.4871

openalex publication_date 2010/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using three different notions of generalized principal eigenvalue of linear\nsecond order elliptic operators in unbounded domains, we derive necessary and\nsufficient conditions for the validity of the maximum principle, as well as for\nthe existence of positive eigenfunctions satisfying Dirichlet boundary\nconditions. Relations between these principal eigenvalues, their simplicity and\nseveral other properties are further discussed.\n

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