Advances in Differential Equations

Diffusive logistic equations in population dynamics

Kazuaki Taira

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The purpose of this paper is to prove an existence and uniqueness theorem of positive solutions of diffusive logistic equations with indefinite weights, which model population dynamics in environments with strong spatial heterogeneity. We prove that the most favorable situations will occur if there is a relatively large favorable region (with good resources and without crowding effects) located some distance away from the boundary of the environment. Moreover we discuss the stability properties for positive steady states.

Article information

Adv. Differential Equations, Volume 7, Number 2 (2002), 237-256.

First available in Project Euclid: 27 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35B35: Stability 35Q80: PDEs in connection with classical thermodynamics and heat transfer 92D25: Population dynamics (general)


Taira, Kazuaki. Diffusive logistic equations in population dynamics. Adv. Differential Equations 7 (2002), no. 2, 237--256.

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