Diamandescu, A. Existence of \(\Psi\)-bounded solutions for linear difference equations on \(\mathbb Z\). (English) Zbl 1178.39018 Electron. J. Qual. Theory Differ. Equ. 2008, Paper No. 26, 13 p. (2008). Summary: We give a necessary and sufficient condition for the existence of \(\Psi\)-bounded solutions for the nonhomogeneous linear difference equation \(x(n + 1) = A(n)x(n) + f(n)\) on \(\mathbb{Z}\). In addition, we give a result in connection with the asymptotic behavior of the \(\Psi\)-bounded solutions of this equation. Cited in 1 Document MSC: 39A22 Growth, boundedness, comparison of solutions to difference equations 39A06 Linear difference equations Keywords:\(\Psi \)-bounded solutions on \(\mathbb Z\); nonhomogeneous linear difference equation; asymptotic behavior PDFBibTeX XMLCite \textit{A. Diamandescu}, Electron. J. Qual. Theory Differ. Equ. 2008, Paper No. 26, 13 p. (2008; Zbl 1178.39018) Full Text: DOI EuDML EMIS