Comparison theorem for a nonlinear boundary value problem on time scales
type: Item
instance of: scholarly article
title: Comparison theorem for a nonlinear boundary value problem on time scales
zbMATH Open document ID: 1012.34018
DOI: 10.1016/S0377-0427(01)00439-3
published in: Journal of Computational and Applied Mathematics
publication date: 2002-06-24T00:00:00Z
review text: The author proves a comparison result for lower and upper solutions \(v(t)\) and \(w(t)\), respectively, to a two-point boundary value problem associated with the second-order dynamic equation \[ -y^{\Delta\Delta}=f(t,y^\sigma,(y^\Delta)^\sigma). \] In particular, sufficient conditions are given so that \(v(t)\leq w(t)\) throughout the considered interval. The proof uses time scales versions of the mean value theorem and the second \(\Delta\)-derivative extremum test. Related work on the mean value theorems appeared in [\textit{S. G. Topal}, J. Difference Equ. Appl. 8, No. 4, 333-343 (2002; Zbl 1006.39016)]. This paper will be useful for researchers interested in lower and upper solutions, and quasilinearization technique for the second-order boundary value problems.
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34E13
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 34B45
zbMATH DE Number: 1758472
zbMATH Keywords: time scale
zbMATH Keywords: two-point boundary value problem
zbMATH Keywords: lower and upper solution
zbMATH Keywords: mean value theorem
author: Gnana Bhaskar Tenali
reviewed by: Roman Šimon Hilscher
MaRDI profile type: Publication
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full work available at URL: s0377-0427(01)00439-3
OpenAlex ID: W2011993371
description: scientific article; zbMATH DE number 1758472