Some stability conditions for scalar Volterra difference equations

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