Bounded and monotone properties of solutions of second-order quasilinear forced difference equations
type: Item
instance of: scholarly article
title: Bounded and monotone properties of solutions of second-order quasilinear forced difference equations
zbMATH Open document ID: 0936.39003
DOI: 10.1016/S0898-1221(99)00186-8
publication date: 2000-01-20T00:00:00Z
review text: The authors consider the quasilinear difference equation (*) \(\Delta(p_{n-1}(\Delta y_{n-1})^\alpha)=q_n y_n^\beta+r_n\), where \(p_0>0\), \(q_0\geq 0\) for \(n\geq N_0\), and \(q_n\not\equiv 0\) for \(n\geq N_1\) for any \(N_1\geq N_0\). Although the results are valid for \(\alpha>0\) and \(\beta>0\), for simplicity of notation the discussion is carried out only in the case \(\alpha\) and \(\beta\) are quotients of odd positive integers. A solution \(y_n\) is of class \(A\) or \(B\) as \(y_n\Delta y_n>0\) or \(y_n\Delta y_n<0\) for some integer \(n\geq N\). If \(r_n\geq 0\), it is shown that every solution of (*) is nonoscillatory and that it belongs either to class \(A\) or class \(B\). A necessary and sufficient condition is given for solutions of class \(A\) to be bounded. A necessary condition is given for the existence of solutions of class \(B\) by means of fixed-point techniques. Lastly, fixed-point and limit-cycle problems are studied. Examples illustrate the results.
reviewed by: Rémi Vaillancourt
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 1391617
zbMATH Keywords: nonoscillatory solution
zbMATH Keywords: monotonicity
zbMATH Keywords: bounded solution
zbMATH Keywords: second-order quasilinear forced difference equations
zbMATH Keywords: fixed-point
zbMATH Keywords: limit-cycle
author: E. Thandapani
author: K. Ravi
MaRDI profile type: Publication
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1391617