Solution of ordinary differential equations by series of delta functions
type: Item
instance of: scholarly article
title: Solution of ordinary differential equations by series of delta functions
zbMATH Open document ID: 0824.34067
DOI: 10.1016/S0022-247X(85)71119-5
author: Luis G. Hernández-Ureña
author: R. Estrada
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-11-09T00:00:00Z
review text: Let \(y(x)\) be a distributional solution of the linear differential equation with polynomial coefficients \[ a_ n(x) y^{(n)}(x)+\cdots+ a_ 0(x) y(x)= 0\tag{1} \] and let \(u(x)= \sum^ \infty_{n= 0} a_ n \delta^{(n)}(x)\) be a formal solution of (1). Here \(\delta(x)\) is the Dirac delta function, \(\delta^{(n)}(x)\) is the distributional derivative of order \(n\) of \(\delta(x)\). The authors establish the relationship between \(u(x)\) and asymptotic expansion of \(y(\lambda x)\) as \(\lambda\to \infty\).
Mathematics Subject Classification ID: 34E05
Mathematics Subject Classification ID: 34A25
zbMATH DE Number: 765148
zbMATH Keywords: distributional solution
zbMATH Keywords: linear differential equation with polynomial coefficients
zbMATH Keywords: formal solution
zbMATH Keywords: Dirac delta function
zbMATH Keywords: asymptotic expansion
MaRDI profile type: Publication
full work available at URL: s0022-247x(85)71119-5
OpenAlex ID: W3151823577
description: scientific article; zbMATH DE number 765148