Boundedness and asymptotic behavior of solutions of a forced difference equation

Abstract

The authors consider the nonlinear difference equation?[yn+pnyn-h]+qnf(yn-k)=rnwhere ?yn=yn+1-yn, {pn}, {qn}, and {rn} are real sequences, and uf(u)>0 for u?0. Sufficient conditions for boundedness and convergence to zero of certain types of solutions axe given. Examples illustrating the results are also included.

Keywords

• difference equations
• nonlinear
• forced
• boundedness
• asymptotic behavior.