Lyapunov-type inequalities for higher-order half-linear difference equations

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.

Sharp Lyapunov-type inequalities for second-order half-linear difference equations with different kinds of boundary conditions

“…Compared to the large number of references to continuous Lyapunov-type inequalities, little has been done for discrete Lyapunov-type inequalities. Let us list the works in which the Lyapunov-type inequality appears in a discrete context: for difference equations see [9][10][11][18][19][20][21]31], for discrete systems see [15,16,26,27,29,30,32], for fractional discrete problems see [12][13][14] and for problems on time scales (as these kind of problems include difference equations) see [1][2][3][4][5][6]17,24].…”

“…Lyapunov-type inequalities for higher order difference equations can be found in [19][20][21]31]. In [21], the second order case reads as follows…”