Dynamics of a Nonlocal Dispersal Model with a Nonlocal Reaction Term.

In this paper, we study a class of nonlocal dispersal problem with a nonlocal term arising in population dynamics: where is a bounded domain, , represents the nonlocal dispersal operator with continuous and non-negative dispersal kernel. The kernel is assumed to be non-negative and is allowed to have a degeneracy in a smooth subdomain of . When is either positive or vanishes in a subdomain, we respectively investigate the existence, multiplicity and asymptotical stability of positive steady states under the local/global variation of parameter by means of sub-supersolution method, Lyapunov-Schmidt reduction, and bifurcation theory. [ABSTRACT FROM AUTHOR]