Existence and uniqueness of steady state solutions of a nonlocal diffusive logistic equation
نویسندگان
چکیده
In this paper, we consider a dynamical model of population biology which is of the classical Fisher type, but the competition interaction between individuals is nonlocal. The existence, uniqueness, and stability of the steady state solution of the nonlocal problem on a bounded interval with homogeneous Dirichlet boundary conditions are studied. Mathematics subject classification (2010). 35K57 · 35B32 · 35B35 · 35B06 · 35Q92 · 92D40.
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Erratum to: Existence and uniqueness of steady state solutions of a nonlocal diffusive logistic equation
We show that the existence of a principal eigenvalue of a linear differential operator claimed in [4] does not always hold; hence, the proof of the stability and uniqueness of positive steady-state solution in [4] are not correct. For the linearized operator (φ ∈ X = {v ∈ C 2 [−1, 1] : v(±1) = 0}) L[φ] = φ (x) + λφ(x) − λφ(x) 1 −1 f (x, y)u(y)dy − λu(x) 1 −1 f (x, y)φ(y)dy, (1) where f ∈ L 2 ((...
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