In this paper, we study the existence of extremal solutions for a nonlinear third-order
differential equation with three-point nonlinear boundary value conditions. By means of the …

Inequalities play a fundamental rôle in all areas of mathematics and their applications.
Among several well-known inequalities, Lyapunov-type inequalities have been studied …

In this article, we obtain Lyapunov-type inequalities for certain odd order linear boundary-
value problems. Our inequalities involve integrals of both q+(t) and q−(t) in addition to that of …

The Lyapunov inequality for second order linear differential equations has been extended to
higher order linear differential equations in various forms. It has also been extended to …

In this paper, we obtain new Lyapunov-type inequalities for the third-order linear differential
equation x+ q (t) x= 0. Our work provides the sharpest results in the literature and makes …

In this paper, we will introduce some new results about Lyapunov type inequalities by
studying the given fractional order Sturm-Liouville problems and fractional order …

In this paper, we consider the existence of multiple solutions for second‐order equation with
Stieltjes integral boundary condition using the three‐critical‐point theorem and variational …

In this paper, first we introduce new definition of conformable fractional derivatives and study
their algebraic properties. As application, we consider certain classes of conformable …

In this paper, we establish the uniqueness and existence of the classical solution to higher-
order boundary value problems. Then, we give a new Lyapunov-type inequalities for higher …

In this paper, we obtain the best constant in the Lyapunov-type inequality for third-order
linear differential equations under the non-conjugate boundary conditions by bounding the …