Fractional Generalized Logistic Equations with Indefinite Weight: Quantitative and Geometric Properties

Marinelli, Alessio; Mugnai, Dimitri

doi:10.1007/s12220-020-00353-x

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2020

2022

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Cited by 3 publications

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“…But for nonlocal situation there are only few results and to the best of our knowledge, all of them consider the case Ψ(-∆) = (−∆) α /2 , the fractional Laplacian (cf. [4,16,25,44,52]). Our results not only generalizes the existing works but also introduces several new methods.…”

Section: Introductionmentioning

confidence: 99%

A study of nonlocal spatially heterogeneous logistic equation with harvesting

Biswas¹,

Modasiya²

2020

Preprint

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We study a class of nonlocal reaction-diffusion equations with a harvesting term where the nonlocal operator is given by a Bernstein function of the Laplacian. In particular, it includes the fractional Laplacian, fractional relativistic operators, sum of fractional Laplacians of different order etc. We study existence, uniqueness and multiplicity results of the solutions to the steady state equation. We also consider the parabolic counterpart and establish the long time asymptotic of the solutions. Our proof techniques rely on both analytic and probabilistic arguments. Ψ(-∆) u = au − f (x, u) − ch(x, u) in D , u = 0 in D c ,

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