Abstract
In this paper, we will establish some new Lyapunov-type inequalities for some higher-order superlinear–sublinear difference equations with boundary conditions. Our results not only complement the existing results established in the literature, but also furnish a handy tool for the study of qualitative properties of solutions of some difference equations.
Highlights
1 Introduction In recent years, there has been an increasing interest in obtaining various classes of inequalities, which play an important role in qualitative analysis of solutions to differential and difference equations; see [1–27]
In the field of inequalities, the Lyapunov-type inequality is one of the fundamental inequalities, which was initially investigated by Lyapunov in 1907
The Lyapunov inequality and its various generalizations were extensively studied by numerous mathematicians
Summary
There has been an increasing interest in obtaining various classes of inequalities, which play an important role in qualitative analysis of solutions to differential and difference equations; see [1–27]. The Lyapunov inequality and its various generalizations were extensively studied by numerous mathematicians. This is due to the fact that these inequalities have proved to be useful tools in the study of oscillation theory, disconjugacy, eigenvalue problems, and many directions of mathematics research areas. Liu and Tang [37] studied the following m-order p-Laplace difference equation: mu(n) p–2 mu(n) + r(n) u(n) p–2u(n) = 0,.
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