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


AKTAŞ M. F. , ÇAKMAK D., Tiryaki A.

APPLIED MATHEMATICS LETTERS, vol.45, pp.1-6, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45
  • Publication Date: 2015
  • Doi Number: 10.1016/j.aml.2014.12.015
  • Journal Name: APPLIED MATHEMATICS LETTERS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1-6
  • Keywords: Lyapunov-type inequalities, Green's functions, Consecutive zeros, LIAPUNOV-TYPE INEQUALITY, NONLINEAR-SYSTEMS, DISFOCALITY
  • Gazi University Affiliated: Yes

Abstract

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.