论文标题
wronskian和参数方法的变化在线性stieltjes微分方程的二阶方程
The Wronskian and the variation of parameters method in the theory of linear Stieltjes differential equations of second order
论文作者
论文摘要
在这项工作中，我们定义了Wronskian和简化的Wronskian的stieltjes衍生物的概念，并以与时间尺度或通常的衍生物相似的方式研究了它们的某些属性。稍后，我们使用这些工具来研究带有stieltjes衍生物的二阶线性微分方程，以找到线性独立的解决方案，并为$ G $ - 连续系数的问题得出参数方法的变化。后来，该理论用一些示例进行了说明，例如对具有分段恒定系数的一维线性Helmholtz方程的研究。
In this work, we define the notions of Wronskian and simplified Wronskian for Stieltjes derivatives and study some of their properties in a similar manner to the context of time scales or the usual derivative. Later, we use these tools to investigate second order linear differential equations with Stieltjes derivatives to find linearly independent solutions, as well as to derive the variation of parameters method for problems with $g$-continuous coefficients. This theory is later illustrated with some examples such as the study of the one-dimensional linear Helmholtz equation with piecewise-constant coefficients.
