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A discrete analogue of Lyapunov-type inequalities for nonlinear systems

✍ Scribed by Mehmet Ünal; Devrim Çakmak; Aydın Tiryaki

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
307 KB
Volume
55
Category
Article
ISSN
0898-1221

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✦ Synopsis

In this paper, by using elementary analysis, we establish some new Lyapunov-type inequalities for nonlinear systems of difference equations when the coefficent β 2 (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.

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