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<p>We consider a parameter dependent periodic-parabolic logistic problem with diffusion involving a degeneracy that replicates time dependent refuges in the habitat of a population. Working under no or very minimal assumptions on the boundary regularity of the domain we show the existence of a unique time-periodic solution which bifurcates with respect to the parameter and show their stability. We show that under suitable assumptions that the periodic solution blows up on part of the domain and remains finite on other parts when the parameter approaches a critical value.</p>

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Logistic growth in seasonally changing environments

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月19日

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  • Daniel Daners,
  • Zeaiter Zeaiter

摘要

We consider a parameter dependent periodic-parabolic logistic problem with diffusion involving a degeneracy that replicates time dependent refuges in the habitat of a population. Working under no or very minimal assumptions on the boundary regularity of the domain we show the existence of a unique time-periodic solution which bifurcates with respect to the parameter and show their stability. We show that under suitable assumptions that the periodic solution blows up on part of the domain and remains finite on other parts when the parameter approaches a critical value.