Expansion in eigenfunctions of a differential operator with nonregular boundary conditions
type: Item
instance of: scholarly article
title: Expansion in eigenfunctions of a differential operator with nonregular boundary conditions
zbMATH Open document ID: 0568.34016
DOI: 10.1007/BF00969850
published in: Lithuanian Mathematical Journal
publication date: 1982-01-01T00:00:00Z
review text: In this paper, considering the differential equation \[ (1)\quad y^{(n)}+a_ 1(x)y^{(n-1)}+(b(x)\lambda +a_ 2(x))y^{(n- 2)}+\sum^{n}_{j=3}a_ j(x)y^{(n-j)}=0 \] and the so-called nonregular boundary conditions (2) \(y^{(k)}(0)=0\), \(k=0,1,...,n-2\), \(y(1)=0\), we prove that any n times continuously differentiable function f(x), satisfying the boundary conditions (2), can be expanded in a uniformly convergent series with respect to the eigenfunctions of the problem (1), (2). We assume that the coefficients \(a_ j(x)\), \(j=1,2,...,n\), have summable derivatives to the (n-j)-th order in the segment [0,1], and \(b(x)>0\) to the (n-2)-nd order.
Mathematics Subject Classification ID: 34L99
Mathematics Subject Classification ID: 34A45
zbMATH DE Number: 3906892
zbMATH Keywords: nonregular boundary conditions
author: Yu. Eh. Degutis
MaRDI profile type: Publication
cites work: Q5624013
full work available at URL: https://doi.org/10.1007/bf00969850
OpenAlex ID: W2067688601
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description: scientific article; zbMATH DE number 3906892