International Journal of Mathematics and Mathematical Sciences 
Volume 17 (1994), Issue 2, Pages 397-400
doi:10.1155/S0161171294000542

Boundedness and asymptotic behavior of solutions of a forced difference equation

John R. Graef and Paul W. Spikes

 Department of Mathematics and Statistics, Mississippi State University, 39762, Mississippi State, MS, USA
Received 3 August 1993

Abstract

The authors consider the nonlinear difference equationΔ[yn+pnyn−h]+qnf(yn−k)=rnwhere Δyn=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.