A discrete analogue of Lyapunov-type inequalities for nonlinear systems

Authors:
Mehmet ínal;Devrim Çakmak;Aydın Tiryaki
Affiliations:
Department of Mathematics and Computer Science, Bahçeşehir University, 34100 Beşiktaş, İstanbul, Turkey;Department of Mathematics Education, Faculty of Education, Gazi University, 06500 Teknikokullar-Ankara, Turkey;Department of Mathematics, Faculty of Arts and Science, Gazi University, 06500 Teknikokullar-Ankara, Turkey
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

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