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<p>In this work, we introduce and investigate a new class of functions called <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mu \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>μ</mi> </math></EquationSource> </InlineEquation>-Stepanov–Orlicz pseudo S-asymptotically <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ω</mi> </math></EquationSource> </InlineEquation>-periodic functions. We establish fundamental properties of this class, including its completeness with respect to the Luxemburg norm and its invariance under translations. We then study the existence and uniqueness of mild solutions to abstract differential equations in Banach spaces with a forcing term belonging to this class. The analysis is based on fixed-point arguments and culminates in an application to a partial differential equation with Dirichlet boundary conditions.</p>

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\(\mu \)-Stepanov–Orlicz pseudo S-asymptotically periodic functions and applications to differential equations

  • 期刊论文

  • 发表日期：

    2026年3月23日

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  • Fatiha Boulahia,
  • Youssef Khemili,
  • Mohsen Miraoui,
  • Mounir Ben Saleh

摘要

In this work, we introduce and investigate a new class of functions called \(\mu \) μ -Stepanov–Orlicz pseudo S-asymptotically \(\omega \) ω -periodic functions. We establish fundamental properties of this class, including its completeness with respect to the Luxemburg norm and its invariance under translations. We then study the existence and uniqueness of mild solutions to abstract differential equations in Banach spaces with a forcing term belonging to this class. The analysis is based on fixed-point arguments and culminates in an application to a partial differential equation with Dirichlet boundary conditions.