Electronic Journal of Differential Equations (May 2017)
Lyapunov-type inequalities for third-order linear differential equations
Abstract
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.
