Sharp Opial‐Type Inequalities Involving Higher Order Derivatives of Two Functions

Agarwal, Ravi P.; Pang, Peter Y. H.

doi:10.1002/mana.19951740102

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1995

2022

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Cited by 14 publications

(2 citation statements)

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“…In 1997, Alzer [13] considered Opial-type inequalities which involve higher-order derivatives of two functions. These generalize earlier results of Agarwal and Pang [14].…”

Section: Introductionsupporting

confidence: 91%

An Opial-Type Inequality on Time Scales

Cheung

2013

Abstract and Applied Analysis

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“…In 1997, Alzer [13] considered Opial-type inequalities which involve higher-order derivatives of two functions. These generalize earlier results of Agarwal and Pang [14].…”

Section: Introductionsupporting

confidence: 91%

An Opial-Type Inequality on Time Scales

Cheung

2013

Abstract and Applied Analysis

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“…In the following, we apply a special case of the inequality with two functions that has been proved by Agarwal and Pang to prove new results by using the maximum value of

(||, Q)

where Q is the antiderivative of q . In this case

Ψ_{1} (Q, r)

and

Ψ_{2} (Q, r)

will be replaced by C 2 and

C_{2}^{*}

defined below.…”

Section: Resultsmentioning

confidence: 99%

Distribution of zeros and disconjugacy of fourth order differential equations

Saker

Kubiaczyk

2015

Mathematische Nachrichten

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Key words Fourth-order differential equations, bending of beams, Opial and Wirtinger inequalities MSC (2010) 34C10, 34K11In this paper, we study the gaps between zeros of nontrivial solutions of fourth order differential equations subject to some boundary conditions, and establish some sufficient conditions for (2, 2)-disconjugacy. The results, which cover some boundary value problems in bending of beams, will be proved by making use of a generalization of Hardy's inequality and some Opial and Wirtinger type inequalities. Some examples are considered to illustrate the main results.

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