一类非齐次线性微分方程的公式解

The Formula Solution of a Family of Nonhomogeneous Linear Differential Equations

本文以K表示具紧支集无穷可微函效全体,K*为其共轭空间。K1*是K*的子空间,其元单侧支集有界,这是一类在工程、物理中很有用的广函。我们在K1*中讨论常系数非齐次线性微分方程,使用广义函数的卷积理论和方程降阶方法,给出这类方程统一的公式解。这种方法非但有理论意义,而且便于实际计算。

In this paper we let K be a set of infinit differentiate funtions with compact supports, K* be its conjugate space and K1* be a subspace of K* which elements’ one-sided supports are bounded.K1* is a kind of very useful generized functions.We discussed the nonhomogeneous linear differential equations with constant coefficient in K1* and gave thier unitary formula solution by use of convolution theory and equation descending order method. This method not only has significance in theory, but also is convenient for actual calculation.