Opial Inequalities with Applications in Differential and Difference Equations

Ravi P. Agarwal, Peter Y. H. Pang (auth.)9780792333654, 0792333659

In 1960 the Polish mathematician Zdzidlaw Opial (1930–1974) published an inequality involving integrals of a function and its derivative. This volume offers a systematic and up-to-date account of developments in Opial-type inequalities. The book presents a complete survey of results in the field, starting with Opial’s landmark paper, traversing through its generalizations, extensions and discretizations. Some of the important applications of these inequalities in the theory of differential and difference equations, such as uniqueness of solutions of boundary value problems, and upper bounds of solutions are also presented.
This book is suitable for graduate students and researchers in mathematical analysis and applications.

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Table of contents :
Front Matter….Pages i-x
Opial’s Inequality….Pages 1-10
Generalizations of Opial’s Inequality….Pages 11-127
Opial Inequalities Involving Higher Order Derivatives….Pages 128-207
Opial Inequalities in Several Independent Variables….Pages 208-282
Discrete Opial Inequalities….Pages 283-355
Applications….Pages 356-389
Back Matter….Pages 390-398