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In this chapter, we present a new result concerning the existence of solutions of a dynamic equation on time scales and also a result on uniqueness of solutions for this type of equations. Moreover, we prove Massera’s type results in order to ensure the existence of periodic solutions for a dynamic equation on time scales defined by a periodic forcing function and taking values in an infinite-dimensional Banach space. Finally, we investigate the real almost periodic solutions of dynamic equations on time scales defined by a periodic forcing function. All these results are completely new in the literature.

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Massera’s Theorem for Nonlinear Dynamic Equations on Time Scales

  • 章节

  • 发表日期：

    2025年

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  • Hernán Henríquez,
  • Jaqueline Godoy Mesquita,
  • Eduard Toon

摘要

In this chapter, we present a new result concerning the existence of solutions of a dynamic equation on time scales and also a result on uniqueness of solutions for this type of equations. Moreover, we prove Massera’s type results in order to ensure the existence of periodic solutions for a dynamic equation on time scales defined by a periodic forcing function and taking values in an infinite-dimensional Banach space. Finally, we investigate the real almost periodic solutions of dynamic equations on time scales defined by a periodic forcing function. All these results are completely new in the literature.