7 research outputs found
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 with two points boundary conditions
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 . 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