On the principal eigenvalue of elliptic operators in $\R^N$ and applications

By Henri Berestychi, Luca Rossi. 2006

78 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ed0184d161161dbfb399c595a443364c20dd0caa

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Reaction-diffusion equations for population dynamics with forced speed I - The case of the whole space (2008, background): “Its properties have been widely investigated in our previous paper [5] and in the one in collaboration with F.”
Spreading speeds for one-dimensional monostable reaction-diffusion equations (2016, background): “The properties of Λ1(L, I) when I is unbounded have been investigated in [7, 10, 11], where it was proved in particular that”
Existence and uniqueness of the solution of a space–time periodic reaction–diffusion equation (2010, background): “Such formulas were used by Berestycki, Nirenberg and Varadhan in [8] and by Berestycki, Hamel and Rossi in [6] in order to generalize the definition of the principal eigenvalue of an elliptic operator to general domains.”
On the definition and the properties of the principal eigenvalue of some nonlocal operators (2015, methodology): “Lately, the search of Liouville type results for semilinear elliptic equations in unbounded domains [10, 56] and the characterisation of spreading speed [7, 48] have stimulated the studies of the properties of λ1(E) and several other notions of principal eigenvalue have emerged.”
Generalizations and Properties of the Principal Eigenvalue of Elliptic Operators in Unbounded Domains (2010, methodology): “In the case of uniformly elliptic operators with bounded smooth coefficients, the inequality λ1 ≤ λ1 was proved in [11] in dimension 1, together with the inequality λ1 ≥ λ1 for self-adjoint operators in dimension less than 4 (subsequently improved to non-smooth operators in [21]).”
Asymptotic spreading in heterogeneous diffusive excitable media (2008, background): “Related notions were defined in [9, 10, 11] for time-independent problems.”