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 differential equations, special cases of which contain the well-known equations such as Emden-Fowler-type and half-linear equations. The inequalities obtained here can be used as handy tools in the study of qualitative behaviour of solutions of the associated equations.

Lyapunov-Type Inequalities for the Quasilinear q-Difference systems

“…In the paper, we consider boundary problem of the following quasilinear q-difference equation [10,11].…”

Lyapunov type inequalities for second-order half-linear differential equations

“…(1.10). Motivated by Yang [14], Lee et al [15], Tiryaki et al [16] and Pachpatte [17], the purpose of this note is to generalize the Lyapunov inequality (1.5) for the second-order linear differential equation (1.1) to the half-linear differential equation (1.8).…”

A Refinement of Lyapunov-Type Inequality for a Class of Nonlinear Systems

“…In [5], Hartman obtained the following inequality: Over the past few decades, there have been many new proofs and generalizations of the inequality (2). It has been generalized to nonlinear second order equations Yong-In Kim [3,10,11], to delay differential equations [2], to higher order differential equations [9,13,14], to discrete linear Hamiltonian systems [4], and so on [6,7,8,12].…”