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<p>We establish flow invariance results for semilinear systems governed by non-Hille–Yosida operators under time-dependent closed convex constraints. A new subtangential condition is introduced, together with explicit sufficient conditions for positive invariance formulated in terms of the resolvent and the nonlinear term. The results apply to systems with non-densely defined operators and time-varying constraints, and are illustrated by applications to an age-structured predator–prey model, a biofilm model, and a class of neutral functional differential equations.</p>

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Time-Dependent Positively Invariant Sets on Cauchy Problems: Applications in Population Dynamics

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月10日

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  • Moustapha Dieye,
  • Ramsès Djidjou-Demasse,
  • Ousmane Seydi

摘要

We establish flow invariance results for semilinear systems governed by non-Hille–Yosida operators under time-dependent closed convex constraints. A new subtangential condition is introduced, together with explicit sufficient conditions for positive invariance formulated in terms of the resolvent and the nonlinear term. The results apply to systems with non-densely defined operators and time-varying constraints, and are illustrated by applications to an age-structured predator–prey model, a biofilm model, and a class of neutral functional differential equations.