Lyapunov-type inequality for a class of odd-order differential equations

Abstract

a b s t r a c tIn this paper, we give a generalization of the well-known Lyapunov-type inequality for a class of odd-order differential equations, the result of this paper is new and generalizes some early results on this topic.

Lyapunov-Type Inequalities for a Conformable Fractional Boundary Value Problem of Order 3<α≤4

“…For other generalizations and extensions of the classical Lyapunov's inequality, we refer the reader to [2,5,[15][16][17][18][19][20][21][22][23] and the references therein.…”

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

“…The first strict inequality in the above inequalities holds since x(t) is not a constant solution (zero solution) of (4) and hence at least one inequalities in (14) or (15) …”

“…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].…”

Lyapunov-Type Inequality for a Class of Discrete Systems with Antiperiodic Boundary Conditions

“…Lyapunov-type inequalities have been proved to be very useful in oscillation theory, disconjugacy, eigenvalue problems, and numerous other applications in the theory of differential and difference equations [1][2][3]. In recent years, there are many literatures which improved and extended the classical Lyapunov inequality including continuous and discrete cases [4][5][6]. Guseinov and Kaymakçalan [7] considered the following discrete Hamiltonian system:…”