TY - GEN

T1 - Global Asymptotic Stability in a Non-autonomous Difference Equation

AU - Ivanov, Anatoli F.

N1 - Funding Information:
Acknowledgements This work was initiated during A. Ivanov’s visit and research stay at the Universidad Nacional de Educación a Distancia, Madrid, in November 2016. He is thankful to Professors D. Franco and J. Perán for their invitation, support and hospitality, as well as for the fruitful discussions that helped shape this paper. The author was also partially supported by the Alexander von Humboldt Stiftung, Germany, during his sabbatical leave from the Pennsylvania State University in the fall 2016, when a substantial part of this research work was accomplished. Principal results of this paper were reported at the International Conference on Difference Equations and Applications held at Technische Universität Dresden, Germany, during May 21–25, 2018.
Publisher Copyright:
© Springer Nature Switzerland AG 2020.

PY - 2020

Y1 - 2020

N2 - Non-autonomous first order difference equation of the form (Formula Presented) is considered where (Formula Presented) is a continuous function satisfying the negative feedback assumption (Formula Presented) and (Formula Presented) is a non-negative sequence. Sufficient conditions for the global asymptotic stability of the zero solution are derived in terms of the attractivity of the fixed point x*=0 under the iterations of distinct maps of the family of one-dimensional maps (Formula Presented) The principal motivation for consideration of the difference equation and the corresponding family of interval maps comes from a problem of asymptotic behavior in differential equations with piece-wise constant argument (DEPCA).

AB - Non-autonomous first order difference equation of the form (Formula Presented) is considered where (Formula Presented) is a continuous function satisfying the negative feedback assumption (Formula Presented) and (Formula Presented) is a non-negative sequence. Sufficient conditions for the global asymptotic stability of the zero solution are derived in terms of the attractivity of the fixed point x*=0 under the iterations of distinct maps of the family of one-dimensional maps (Formula Presented) The principal motivation for consideration of the difference equation and the corresponding family of interval maps comes from a problem of asymptotic behavior in differential equations with piece-wise constant argument (DEPCA).

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U2 - 10.1007/978-3-030-35502-9_10

DO - 10.1007/978-3-030-35502-9_10

M3 - Conference contribution

AN - SCOPUS:85080907049

SN - 9783030355012

T3 - Springer Proceedings in Mathematics and Statistics

SP - 231

EP - 250

BT - Difference Equations and Discrete Dynamical Systems with Applications - 24th ICDEA 2018

A2 - Bohner, Martin

A2 - Siegmund, Stefan

A2 - Šimon Hilscher, Roman

A2 - Stehlík, Petr

PB - Springer

T2 - 24th International Conference on Difference Equations and Applications, ICDEA 2018

Y2 - 21 May 2018 through 25 May 2018

ER -