Abstract
It is well known that the set of positive solutions may contain crucial clues for the stationary patterns. In this paper, we consider a class of diffusive logistic equations with nonlocal terms subject to the Dirichlet boundary condition in a bounded domain. We study the existence of positive solutions under certain conditions on the parameters by using bifurcation theory. Finally, we illustrate the general results by applications to models with one-dimensional spatial domain.
Highlights
Many researchers pay more attention on the studies of reaction-diffusion equations; we refer to, for example, [ – ]
Positive solutions correspond to the existence of steady states of species
It is well known that the set of positive solutions may contain crucial clues for the stationary patterns
Summary
Many researchers pay more attention on the studies of reaction-diffusion equations; we refer to, for example, [ – ]. Positive solutions correspond to the existence of steady states of species. Applying the implicit function theorem, Chen and Shi [ ] obtained the existence and uniqueness of a positive steady-state solution of system
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