A discrete analogue of Lyapunov-type inequalities for nonlinear systems

Abstract

In this paper, by using elementary analysis, we establish some new Lyapunov-type inequalities for nonlinear systems of difference equations when the coefficent β<inf>2</inf> (t) is not necessarily nonnegative valued and when the end points are not necessarily usual zeros, but rather, generalized zeros. Applying these inequalities, we obtain a disconjugacy criterion and boundedness for the solution of our system. Some special cases of our results contain recently developed Lyapunov inequalities for discrete linear Hamiltonian systems. The inequalities obtained here can be used as handy tools in the study of the qualitative behaviour of solutions of the associated equations. © 2007 Elsevier Ltd. All rights reserved. © 2008 Elsevier B.V., All rights reserved.