时标意义下微分方程的常数变易法  

Variation of Constants of Differential Equations On Time Scales

作　　者：詹再东[1] 刘桂珍[1] 

机构地区：[1]贵州大学理学院,贵州贵阳550025

出　　处：《贵州大学学报（自然科学版）》2008年第3期225-229,共5页Journal of Guizhou University:Natural Sciences

基　　金：国家自然科学基金资助(No.10661004)

摘　　要：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.

关 键 词：常数变易法 时标下常微分方程 通解公式. 

分 类 号：O175.1[理学—数学]