منابع مشابه
An Opial-type inequality with an integral boundary condition
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.
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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.
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In this article we give different sufficient conditions for inequality (∫ b a f(x)dx )β ≥ ∫ b a f(x)dx to hold.
متن کاملOn an Opial Inequality with a Boundary Condition
R.C. Brown conjectured (in 2001) that the Opial-type inequality
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.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1962
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1962-0139706-1