Abstract An impulse nonlinear problem admitting discontinuous solutions that are functions of bounded variation is studied. This problem models the deformation of a discontinuous string (chains of strings fastened together by springs) with elastic supports in the form of linear and nonlinear springs (for example, springs with different turns, whose deformations do not obey Hooke’s law). The model is described by a second-order differential equation with derivatives in special measures and Dirichlet boundary conditions. Existence theorems are proved, and conditions for the existence of nonnegative solutions are obtained.

中文翻译：

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脉冲非线性问题中的 Stieltjes 微分

摘要 研究了一个允许作为有界变分函数的不连续解的脉冲非线性问题。该问题模拟了具有线性和非线性弹簧形式的弹性支撑的不连续弦（由弹簧紧固在一起的弦）的变形（例如，具有不同匝数的弹簧，其变形不遵循胡克定律）。该模型由二阶微分方程描述，该方程具有特殊测度和狄利克雷边界条件的导数。证明了存在定理，得到了非负解存在的条件。