Electron. J. Differential Equations, Vol. 2017 (2017), No. 139, pp. 1-14.

Lyapunov-type inequalities for third-order linear differential equations

Mustafa Fahri Aktas, Devrim Cakmak

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.

Submitted January 5, 2017. Published May 24, 2017.
Math Subject Classifications: 34C10, 34B05, 34L15.
Key Words: Lyapunov-type inequalities; Green's Functions; three-point boundary conditions.

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Mustafa Fahri Aktas
Gazi University, Faculty of Sciences
Department of Mathematics
06500 Teknikokullar, Ankara, Turkey
email: mfahri@gazi.edu.tr
Devrim Cakmak
Gazi University, Faculty of Education
Department of Mathematics Education
06500 Teknikokullar, Ankara, Turkey
email: dcakmak@gazi.edu.tr

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