Opuscula Math. 36, no. 4 (2016), 459-470

Opuscula Mathematica

Some stability conditions for scalar Volterra difference equations

Leonid Berezansky
Małgorzata Migda
Ewa Schmeidel

Abstract. New explicit stability results are obtained for the following scalar linear difference equation \[x(n+1)-x(n)=-a(n)x(n)+\sum_{k=1}^n A(n,k)x(k)+f(n)\] and for some nonlinear Volterra difference equations.

Keywords: linear and nonlinear Volterra difference equations, boundedness of solutions, exponential and asymptotic stability.

Mathematics Subject Classification: 34A10, 39A22, 39A30.

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  • Leonid Berezansky
  • Ben-Gurion University of Negev, Department of Mathematics, Beer-Sheva, 84105 Israel
  • Małgorzata Migda
  • Poznan University of Technology, Institute of Mathematics, Piotrowo 3A, 60-965 Poznań, Poland
  • Ewa Schmeidel
  • University of Bialystok, Institute of Mathematics, Faculty of Mathematics and Computer Science, Ciołkowskiego 1M, 15-245 Białystok, Poland
  • Communicated by Marek Galewski.
  • Received: 2015-12-01.
  • Revised: 2016-01-04.
  • Accepted: 2016-02-10.
  • Published online: 2016-04-01.
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Cite this article as:
Leonid Berezansky, Małgorzata Migda, Ewa Schmeidel, Some stability conditions for scalar Volterra difference equations, Opuscula Math. 36, no. 4 (2016), 459-470, http://dx.doi.org/10.7494/OpMath.2016.36.4.459

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