Lyapunov-type inequalities for n-dimensional quasilinear systems

In this article, inspired by the paper of Yang et al [12], we establish new versions of Lyapunov-type inequalities for a certain class of Dirichlet quasilinear systems

LYAPUNOV-TYPE INEQUALITIES FOR THIRD-ORDER LINEAR DIFFERENTIAL EQUATIONS

In this article, we establish new Lyapunov-type inequalities for third-order linear differential equations y `''+q(t)y = 0 under the three-point boundary conditions y(a) = y(b) = y(c) = 0 and y(a) = y `'(d) = y(b) = 0 by bounding Green's functions G (t; s) corresponding to appropriate boundary conditions. Thus, we obtain the best constants of Lyapunov-type inequalities for three-point boundary value problems for third-order linear differential equations in the literature

Lyapunov-type inequalities for nonlinear systems involving the (p1,p2,...,pn)-Laplacian

We prove some generalized Lyapunov-type inequalities for n-dimensional Dirichlet nonlinear systems. We extend the results obtained by Cakmak and Tiryaki [6] for a parameter $1<p_k<2$. As an application, we obtain lower bounds for the eigenvalues of the corresponding system

On the Lyapunov-type inequalities of a three-point boundary value problem for third order linear differential equations

In this paper, by using Green's function for second order differential equations with Dirichlet boundary condition, we establish new Lyapunov-type inequalities for third order linear differential equation which improve all existing results in the literature. As an application, we obtain sharp lower bound for the eigenvalues of corresponding equations and for the distance between the end points in the three consecutive zeros of the solution of the equations. (C) 2015 Elsevier Ltd. All rights reserved

On Lyapunov-type inequalities for odd order boundary value problems

In this article, we construct new Lyapunov-type inequalities for odd order boundary value problems. The aim of this article is to find the maximum of Green's function |G2n+1(x,s)| corresponding to two-point boundary value problems. To the best of our knowledge, there is no paper dealing with Lyapunov-type inequalities for odd order boundary value problems by bounding the Green's function of the same problem. In addition, some applications of the obtained inequalities are also given