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Existence of \(\Psi\)-bounded solutions for linear difference equations on \(\mathbb Z\). (English) Zbl 1178.39018

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.

MSC:

39A22 Growth, boundedness, comparison of solutions to difference equations
39A06 Linear difference equations
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