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<p>We investigate pseudo-almost periodic solutions for a class of nonautonomous difference equations in Banach spaces. Using discrete evolution family techniques combined with convolution operators, we establish existence and uniqueness results for linear systems driven by Stepanov pseudo-almost periodic forcing terms. These results are further extended to nonlinear equations under suitable Lipschitz conditions, ensuring the existence of unique pseudo-almost periodic mild solutions. As applications, we examine both a discrete heat equation with time-dependent coefficients and a discrete parabolic integrodifference equation with memory, demonstrating that pseudo-almost periodicity and Stepanov pseudo-almost periodicity are preserved in the long-term dynamics of these discrete systems.</p>

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Pseudo-almost Periodic and Stepanov Solutions of Discrete Evolution Equations with Applications

  • 期刊论文

  • 发表日期：

    2026年7月23日

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  • Dhaou Lassoued

摘要

We investigate pseudo-almost periodic solutions for a class of nonautonomous difference equations in Banach spaces. Using discrete evolution family techniques combined with convolution operators, we establish existence and uniqueness results for linear systems driven by Stepanov pseudo-almost periodic forcing terms. These results are further extended to nonlinear equations under suitable Lipschitz conditions, ensuring the existence of unique pseudo-almost periodic mild solutions. As applications, we examine both a discrete heat equation with time-dependent coefficients and a discrete parabolic integrodifference equation with memory, demonstrating that pseudo-almost periodicity and Stepanov pseudo-almost periodicity are preserved in the long-term dynamics of these discrete systems.