An Opial-type inequality with an integral boundary condition
نویسندگان
چکیده
We determine the best constant K and extremals of the Opial-type inequality ∫ b a |yy ′| dx ≤ K(b − a) ∫ b a |y ′|2 dx where y is required to satisfy the boundary condition ∫ b a y dx = 0. The techniques employed differ from either those used recently by Denzler to solve this problem or originally to prove the classical inequality; but they also yield a new proof of that inequality.
منابع مشابه
On an Opial Inequality with a Boundary Condition
R.C. Brown conjectured (in 2001) that the Opial-type inequality
متن کاملOn Opial–type Integral Inequalities and Applications
In the present paper we establish some new Opial-type inequalities involving higher order partial derivatives. Our results in special cases yield some of the recent results on Opial’s inequality. As application, we prove the uniqueness of the solution of initial value problem involving higher order partial differential equation. Mathematics subject classification (2010): 26D15.
متن کاملAn Opial–type Inequality for Fractional Derivatives of Two Functions
This paper presents improvements of some Opial-type inequalities involving the RiemannLiouville, Caputo and Canavati fractional derivatives, and presents some new Opial-type inequalities. Mathematics subject classification (2010): 26A33, 26D15.
متن کاملOn a Discrete Opial-type Inequality
The main purpose of the present paper is to establish a new discrete Opial-type inequality. Our result provide a new estimates on such type of inequality.
متن کاملA Multiple Opial Type Inequality for the Riemann–liouville Fractional Derivatives
The aim of this paper is to prove a multiple Opial type inequality for RL fractional derivatives which is proved for two factors and ordinary derivatives by Fink in [6]. Two methods are applied and a comparison of the obtained estimations is also given.
متن کامل