Sign properties of Green's functions for disconjugate dynamic equations on time scales.
type: Item
instance of: scholarly article
title: Sign properties of Green's functions for disconjugate dynamic equations on time scales.
zbMATH Open document ID: 1054.34023
DOI: 10.1016/S0022-247X(02)00579-6
author: Paul W. Eloe
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-01-06T00:00:00Z
review text: The author studies a two-point boundary value problem associated with the higher-order dynamic equation \[ y^{\Delta^n}+\sum_{i=1}^n q_i(t)\, \left( y^{\Delta^{n-i}} \right)^\sigma =0 \] on a time scale interval \([a,b]\). The author uses the concepts of a generalized zero (of order greater or equal to \(k\)), disconjugacy, and factorization to establish sign properties of the corresponding Green's functions. The results generalize and unify the corresponding continuous-time and discrete-time results. Anyone interested in the qualitative theory of differential, difference, and/or dynamic equations on time scales will find this paper useful.
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34B27
Mathematics Subject Classification ID: 39A12
zbMATH DE Number: 2022068
zbMATH Keywords: time scale
zbMATH Keywords: generalized zero
zbMATH Keywords: disconjugacy
zbMATH Keywords: Green's function
zbMATH Keywords: maximum principle
reviewed by: Roman Šimon Hilscher
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2022068