The effects of degeneracy on nonlocal dispersal logistic equations. (August 2021)

• Record Type: Journal Article
• Authors: Sun, Jian-Wen; You, Chunmei; Qiao, Shao-Xia
• Is Part Of: Nonlinear analysis. Volume 60(2021)
• Publication Date: 2021-08
• Subjects: Nonlocal dispersal -- Positive solution -- Degeneracy; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103300
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper is concerned with the nonlocal dispersal logistic equation J ∗ u ( x ) − u ( x ) = − λ u ( x ) + a ( x ) u p in Ω ̄, u ( x ) = 0 in R N ∖ Ω ̄, where Ω ⊂ R N ( N ≥ 1 ) is a bounded domain, λ and p > 1 are constants, the dispersal kernel J and the coefficient a ( x ) are nonnegative. The work of García-Melián and Rossi (2009) reveals that the nonlocality makes a key change of positive solutions. In this paper, we investigate the sharp effects of degeneracy on the behavior of positive solutions. We find that the effect is different from the diffusive logistic equation.