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Proceedings of the American Mathematical Society
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Article . 2018
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Massera’s theorem in quantum calculus

Massera's theorem in quantum calculus
Authors: Martin Bohner; Jaqueline G. Mesquita;

Massera’s theorem in quantum calculus

Abstract

The authors present \(q\)-versions of Massera's theorem for different types of \(q\)-difference equations. Let \(f^{\Delta}(t)\) denote the usual \(q\)-derivative (also known as Jackson derivative). For the linear \(q\)-difference equation \(f^{\Delta}(t)=a(t)f(t)+b(t)/t\) they derive a periodicity result using Brouwer's fixed point theorem. Precisely, such an \(\omega\)-periodic linear \(q\)-difference equation has an \(\omega\)-periodic solution iff it has a \(q\)-bounded solution. The second main result is a version of Massera's theorem for nonlinear \(q\)-difference equations of the form \(f^{\Delta}(t)=g(t,tf(t))\): under certain assumptions they show that if such an equation has a \(q\)-bounded solution, then it has an \(\omega\)-periodic solution.

Related Organizations
Keywords

\(q\)-calculus and related topics, Difference equations, scaling (\(q\)-differences), Stability theory for difference equations, Massera's theorem, $q$-difference equation, Periodic solutions of difference equations

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
12
Top 10%
Top 10%
Average
hybrid