Generalizations and Properties of the Principal Eigenvalue of Elliptic Operators in Unbounded Domains

By Henri Berestycki, Luca Rossi. 2010

117 citations recorded by the source corpus.

Using three different notions of the generalized principal eigenvalue of linear second‐order elliptic operators in unbounded domains, we derive necessary and sufficient conditions for the validity of the maximum principle, as well as for the existence of positive eigenfunctions for the Dirichlet problem. Relations between these principal eigenvalues, their simplicity, and several other properties are further discussed. © 2015 Wiley Periodicals, Inc.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/63a7429af2617c0025c7ba739c2a00a689e93894

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In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Persistence versus extinction under a climate change in mixed environments (2014, methodology): “genfunction of the problem −∆ϕR − c∂1ϕR −fs(x,0)ϕR = λRϕR x∈ ΩR ϕR(x1,y) = 0 |x1| <R,y∈ ∂ω ϕR(±R,y) = 0 y∈ ω, we deduce, by Theorem 1.9 in [11], that λD = limR→∞ λR. Note that Theorem 1.9 in [11] also deals with the case of nonsmooth domain as the set ΩR of ours. Then the existence of Eq. (46)”
On the definition and the properties of the principal eigenvalue of some nonlocal operators (2015, methodology): “It is also an important tool in the characterisation of maximum principle properties satisfies by elliptic operators [12, 8] and to describe continuous semi-groups that preserve an order [1, 32, 46].”