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
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.