The effects of degeneracy on nonlocal dispersal logistic equations. (August 2021) - Sun, Jian-Wen; You, Chunmei; Qiao, Shao-Xia
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.