时标意义下微分方程的常数变易法

Variation of Constants of Differential Equations On Time Scales

主要研究时标意义下的线性常微分方程解的常数变易法,同经典处理方式一样,通过齐次通解进行常数变易法直接导出时间模上非齐次线性常微分方程的解。证明出时标下高阶线性微分方程解的存在唯一性,并通过Wronskians行列式和Cramer法则得到其通解公式。

We study the variation of constants of solutions to linear differential equations on time scales. Similar to classical methods we can obtain the general solution of the inhomogeneous equation on time scales from the general solution of corresponding homogeneous equation though variation of constants. We prove the existence and uniqueness of solution to higher-order linear differential equation, and get the general solution by Wronskians determinant and Cramer rule.