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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