Explicit bounds for linear difference equations /

by 1981- Goedhart, Eva Govinda

This thesis provides explicit, applicable bounds for solutions of a wide class of second-order difference equations with nonconstant coefficients. Among the applications is an affirmative answer to a question of Stevi?. We also present bounds for second-order difference equations with positive restricted (nonconstant) coefficients. It is determined that whenever the coefficients of the associated monic equation are less than the constant (1/3)1/3, all solutions tend to zero at an exponential rate. This constant is optimal. Some further asymptotic results and optimal explicit inequalities are also given. We then extend our results to give explicit, applicable bounds for solutions of a wide class of third-order difference equations with nonconstant coefficients. The techniques used are readily adaptable for higher order equations. iii