Boundedness and stability in nonlinear delay difference equations employing fixed point theory

M. Islam, University of Dayton, Dayton, U.S.A.
E. Yankson, University of Dayton, Dayton, U.S.A.

E. J. Qualitative Theory of Diff. Equ., No. 26. (2005), pp. 1-18.

Abstract: In this paper we study stability and boundedness of the nonlinear difference equation
\begin{equation} x(t+1)=a(t)x(t)+c(t)\Delta x(t-g(t))+q(x(t),x(t-g(t))\big).\nonumber \end{equation}
In particular we study equi-boundedness of solutions and the stability of the zero solution of this equation. Fixed point theorems are used in the analysis.

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