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

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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About the authors ▼
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
About the article ▼
Communicated by Marek Galewski.
Received: 2015-12-01.
Revised: 2016-01-04.
Accepted: 2016-02-10.
Published online: 2016-04-01.
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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