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Abstract <p> The article considers the Hyers–Ulam–Rassias stability property for nonlinear systems of differential equations with a generalized action on the right-hand side. Since the right-hand side of the systems under consideration is unbounded, the standard definition of the stability property under consideration cannot be used. A formalization of the Hyers–Ulam–Rassias stability concept for nonlinear systems of differential equations with delay and discontinuous trajectories is given. Sufficient conditions are obtained that ensure such stability for a nonlinear system of differential equations with delay and a generalized action on the right-hand side. </p>

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On the Hyers–Ulam–Rassias Stability of Nonlinear Differential Equations Containing Products of Discontinuous and Generalized Functions and Delays

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • A. N. Sesekin,
  • A. D. Kandrina,
  • N. V. Gredasova

摘要

Abstract

The article considers the Hyers–Ulam–Rassias stability property for nonlinear systems of differential equations with a generalized action on the right-hand side. Since the right-hand side of the systems under consideration is unbounded, the standard definition of the stability property under consideration cannot be used. A formalization of the Hyers–Ulam–Rassias stability concept for nonlinear systems of differential equations with delay and discontinuous trajectories is given. Sufficient conditions are obtained that ensure such stability for a nonlinear system of differential equations with delay and a generalized action on the right-hand side.