Zeitschrift für angewandte Mathematik und Physik

, Volume 64, Issue 4, pp 1267–1278 | Cite as

Existence and uniqueness of steady state solutions of a nonlocal diffusive logistic equation

Article

Abstract

In this paper, we consider a dynamical model of population biology which is of the classical Fisher type, but the competition interaction between individuals is nonlocal. The existence, uniqueness, and stability of the steady state solution of the nonlocal problem on a bounded interval with homogeneous Dirichlet boundary conditions are studied.

Mathematics subject classification (2010)

35K57 35B32 35B35 35B06 35Q92 92D40 

Keywords

Nonlocal influence Reaction-diffusion equation Logistic equation Steady state solution Stability 

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Copyright information

© Springer Basel 2012

Authors and Affiliations

  1. 1.Y.Y.Tseng Functional Analysis Research CenterHarbin Normal UniversityHarbinPeople’s Republic of China
  2. 2.Department of MathematicsHeihe UniversityHeihePeople’s Republic of China
  3. 3.Department of MathematicsCollege of William and MaryWilliamsburgUSA

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