Journal ArticleDOI
Sharp Opial-Type Inequalities Involving Higher Order Derivatives of Two Functions
Ravi P. Agarwal,Peter Y. H. Pang +1 more
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In this article, a very general Opial-type inequalities involving higher-order derivatives of two functions are presented, and extended and improved versions of several recent results are derived from these inequalities.Abstract:
In this paper we shall offer very general Opial-type inequalities involving higher order derivatives of two functions. From these inequalities we then deduce extended and improved versions of several recent results.read more
Citations
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Journal ArticleDOI
Opial type inequalities involving Riemann-Liouville fractional derivatives of two functions with applications
TL;DR: Applications of some of these special inequalities are given in establishing uniqueness of solution and in giving upper bounds to solutions of initial value fractional problems involving a very general system of two fractional differential equations.
Journal ArticleDOI
Opial type inequalities involvingfractional derivatives of two functions and applications
TL;DR: In this paper, a large variety of very general, but basic L"p (1 < p < ~) form, Opial type inequalities are established involving generalized fractional derivatives of two functions in different orders and powers.
Journal ArticleDOI
An Opial-type inequality involving higher-order derivatives of two functions
TL;DR: In this paper, the constant in an Opial-type inequality involving higher-order derivatives of two functions was improved, which was due to Agarwal and Pang, who improved the constant due to their work.
Book ChapterDOI
Opial-Type Inequalities Involving Higher Order Derivatives
Ravi P. Agarwal,Peter Y. H. Pang +1 more
TL;DR: The first generalization of Opial's inequality (1.1) was due to Das as discussed by the authors, who improved Das' results and further extensions which appeared one year later paved the way for the many subsequent results of this type.
Journal ArticleDOI
Properties of solutions of fourth-order differential equations with boundary conditions
TL;DR: In this article, the authors established sufficient conditions for -disconjugacy and study the distribution of zeros of nontrivial solutions of fourth-order differential equations, and extended the results to cover some boundary value problems in bending of beams.
References
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Book
Inequalities Involving Functions and Their Integrals and Derivatives
TL;DR: Gronwall inequalities in higher dimension as mentioned in this paper have been used to prove integral inequalities in other spaces: discrete, functional and abstract, and they have been shown to hold for functions with bounded derivatives.
Book
Opial Inequalities with Applications in Differential and Difference Equations
P.Y. Pang,Ravi P. Agarwal +1 more
TL;DR: In this paper, generalizations of Opial's Inequality are discussed, including Opial Inequalities Involving Higher Order Derivatives and Discrete Opial inequalities in Several Independent Variables.
Journal ArticleDOI
Opial-type integral inequalities involving several higher order derivatives
TL;DR: In this article, the authors established for the first time Opial-type integral inequalities involving a function and several higher order derivatives, which contain some known results of P. R. Beesack and K. M. Das.
Journal ArticleDOI
On Opial-type integral inequalities
TL;DR: In this article, the authors established new integral inequalities involving two functions and their first order and higher order derivatives, and derived the Opial inequality and some of its generalizations in the special cases.
Journal ArticleDOI
An inequality similar to Opial’s inequality
TL;DR: In this article, a sharper version of Opial's original inequality was obtained for linear differential equations of order n, where y(n-1) = O for i=O, 1, n -1 where n? 1.