91 citations · 228 across the 32 of their papers we have counts for
39 papers
Uniqueness and multiplicity for semilinear elliptic problems in unbounded domains
Henri Berestycki, Cole Graham, Juncheng Wei
We study the influence of geometry on semilinear elliptic equations of bistable or nonlinear-field type in unbounded domains. We discover a surprising dichotomy between epigraphs t…
Generalized principal eigenvalues for parabolic operators in bounded domains
Henri Berestycki, Grégoire Nadin, Luca Rossi
We introduce here new generalized principal eigenvalues for linear parabolic operators with heterogeneous coefficients in space and time. We consider a bounded spatial domain and a…
A stable-compact method for qualitative properties of semilinear elliptic equations
Henri Berestycki, Cole Graham
We study the uniqueness of reaction-diffusion steady states in general domains with Dirichlet boundary data. Here we consider "positive" (monostable) reactions. We describe geometr…
Biological invasions and epidemics with nonlocal diffusion along a line
Henri Berestycki, Jean-Michel Roquejoffre, Luca Rossi
The goal of this work is to understand and quantify how a line with nonlocal diffusion given by an integral enhances a reaction-diffusion process occurring in the surrounding plane…
The steady states of strong-KPP reactions in general domains
Henri Berestycki, Cole Graham
We study the uniqueness of steady states of strong-KPP reaction--diffusion equations in general domains under various boundary conditions. We show that positive bounded steady stat…
Reaction-diffusion equations in the half-space
Henri Berestycki, Cole Graham
We study reaction-diffusion equations of various types in the half-space. For bistable reactions with Dirichlet boundary conditions, we prove conditional uniqueness: there is a uni…