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<p>In this paper, we deal with the semilinear impulsive evolution equation with nonlocal condition in a reflexive Banach space. By establishing and solving a family of approximating problem and applying the Leray–Schauder continuation principle, we obtain the existence and uniqueness of mild solution for impulsive nonlocal problem under that nonlinearity satisfies Carathéodory condition. Finally, our main results are applied to a class of superlinear parabolic problems.</p>

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Existence of mild solutions for impulsive evolution equation with nonlocal condition

  • 期刊论文

  • 发表日期：

    2025年4月9日

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  • Weifeng Ma,
  • Yongxiang Li

摘要

In this paper, we deal with the semilinear impulsive evolution equation with nonlocal condition in a reflexive Banach space. By establishing and solving a family of approximating problem and applying the Leray–Schauder continuation principle, we obtain the existence and uniqueness of mild solution for impulsive nonlocal problem under that nonlinearity satisfies Carathéodory condition. Finally, our main results are applied to a class of superlinear parabolic problems.