Mathematics

CLC number: O316

Generalized Gradient Method for the Stability of Solutions to Herglotz-Type Equations for Non-Autonomous Non-Conservative Systems

非自治非保守系统Herglotz型方程解稳定性的广义梯度方法

¹ School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou 215009, Jiangsu, China
² College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, Jiangsu, China

^† Corresponding author. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 4 June 2025

Abstract

The stability of solutions of Herglotz-type equations for non-autonomous non-conservative systems is studied by means of generalized gradient method. Firstly, Herglotz-type equations for non-conservative systems are given and expressed as contravariant algebraic form. Secondly, two classes of generalized gradient systems are introduced. Thirdly, the conditions for the transformation of Herglotz-type equations into generalized gradient systems are given, and the solutions of Herglotz-type equations and the stability of the solutions are analyzed. Finally, for each case discussed in this paper, the calculation process is demonstrated in detail to show that the method is effective.

摘要

本文利用广义梯度方法研究了非自治非保守系统Herglotz型方程解的稳定性。首先，给出了非保守系统的Herglotz型方程，并将其表示为逆变代数形式。其次，介绍了两类广义梯度系统。第三，给出了Herglotz型方程转化为广义梯度系统的条件，并分析了Herglotz型方程的解以及解的稳定性。最后，针对文中所讨论的每种情形，通过算例详细展示了其计算过程，也验证了方法的有效性。