PORTUGALIAE MATHEMATICA Vol. 52, No. 4, pp. 379390 (1995) 

The Linear Cauchy Problem for a Class of Differential Equations with Distributional CoefficientsC.O.R. SarricoCentro de Matemática e Aplicaç\ oes Fundamentais,Av. Prof. Gama Pinto, 2, 1699 Lisboa Codex  PORTUGAL Abstract: We consider the problem $X^{(n)}=\sum_{i=1}^{n}U_{i}X^{(ni)}+V$, $X^{(ni)}(t_{0})=a_{i}$ in dimension 1 ($X\in\calc{D}'$ is unknown, $n$ is a positive integer, $V\in\calc{D}'$, $U_{1},...,U_{n}\in C^{\infty}\oplus \calc{D}_{m}^{\prime p}$, $\calc{D}_{m}^{\prime p}=\calc{D}^{\prime p}\cap \calc{D}_{m}'$, $\calc{D}^{\prime p}$ is the space of distributions of order $\le p$ in the sense of Schwartz, $\calc{D}_{m}'$ is the space of distributions with nowheredense support, $a_{1},...,a_{n}\in\C$ and $t_{0}\in\R$). Keywords: Ordinary differential equations; products of distributions; distributions, generalized functions. Classification (MSC2000): 34A30; 46F10 Full text of the article:
Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.
© 1995 Sociedade Portuguesa de Matemática
