The dynamics of a diffusive logistic model with nonlocal terms

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• 作者：Xianhua Xie ; Li Ma
• 关键词：logistic model ; positive steady ; state solutions ; a priori bounds ; bifurcation theory
• 刊名：Advances in Difference Equations
• 出版年：2017
• 出版时间：December 2017
• 年：2017
• 卷：2017
• 期：1
• 全文大小：1633KB
• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847
• 卷排序：2017

文摘

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.