Lyapunov-type inequalities for third-order linear and half-linear difference equations and extensions

Abstract

We derive Lyapunov-type inequalities for third-order half-linear difference equations. The results are significant as the existing work on Lyapunov-type inequalities for difference equations is limited only to even order cases. As the techniques for even order difference equations are not applicable to odd order difference equations, the methods used here are novel. The resulting inequalities utilize and . New results for linear difference equations are obtained as a special case and are further extended to more general linear equations. Moreover, brief discussions are also given for third-order backward difference equations and dynamic equations on time scales.