Scholarlink

<p>In this work, we are concerned in investigating periodic solutions of parametric classes of first- and second-order state-dependent abstract-retarded functional differential equations with infinite delay. To achieve this, we employ the theory of strongly continuous semigroups of operators for first-order equations and the theory of cosine functions of operators for second-order equations. By combining these theories with the concept of topological degree, we successfully establish the existence of periodic solutions for a distinct class of first- and second-order parametric equations. To illustrate our abstract formulation, given its significance in various biological processes, we apply the main result to a class of transport equations with state-dependent delay.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Periodic solutions of state-dependent abstract functional differential equations with infinite delay

  • 期刊论文

  • 发表日期：

    2025年7月29日

查看全文
  • Claudio A. Gallegos,
  • Hernán R. Henríquez,
  • Verónica Poblete

摘要

In this work, we are concerned in investigating periodic solutions of parametric classes of first- and second-order state-dependent abstract-retarded functional differential equations with infinite delay. To achieve this, we employ the theory of strongly continuous semigroups of operators for first-order equations and the theory of cosine functions of operators for second-order equations. By combining these theories with the concept of topological degree, we successfully establish the existence of periodic solutions for a distinct class of first- and second-order parametric equations. To illustrate our abstract formulation, given its significance in various biological processes, we apply the main result to a class of transport equations with state-dependent delay.