Optimal existence results for \(n\)th order periodic boundary value difference equations
type: Item
instance of: scholarly article
title: Optimal existence results for \(n\)th order periodic boundary value difference equations
zbMATH Open document ID: 0962.39006
author: Alberto Cabada
author: Victoria Otero-Espinar
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-06-14T00:00:00Z
review text: The authors study the \(n\)-th order nonlinear difference equation \[ u(k+n)= f\bigl(k,u(k), \dots,u(k+n) \bigr),\;k\in\{0, \dots, N-1\}, \] with periodic boundary conditions. Supposing that there exist ordered lower and upper solutions, they obtain a solution for this problem. The existence results are equivalent to finding the values of \(K_i\), \(i=1, \dots,n\), for which the linear operator \[ u(k+n)+ \sum^n_{i=0} K_iu(k+i) \] in the space of periodic functions is an inverse positive operator. Moreover an expression of the Green function is obtained. Applications to the first and second order equations are included.
reviewed by: Dobiesław Bobrowski
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A70
zbMATH DE Number: 1497289
zbMATH Keywords: difference operator
zbMATH Keywords: periodic solutions
zbMATH Keywords: nonlinear difference equation
zbMATH Keywords: periodic boundary conditions
zbMATH Keywords: lower and upper solutions
zbMATH Keywords: inverse positive operator
zbMATH Keywords: Green function
MaRDI profile type: Publication
full work available at URL: jmaa.2000.6824
OpenAlex ID: W2035611208
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DOI: 10.1006/JMAA.2000.6824
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description: scientific article; zbMATH DE number 1497289