Integral and Discrete Inequalities and Their Applications
Volume I: Linear Inequalities
Volume II: Nonlinear Inequalities

Authors: Yuming Qin





Collects integral and discrete inequalities established by many different authors

Presents some integral and discrete inequalities and their applications in (partial) differential equations, integral equations and discrete equations

Introduces Gronwall-Bellman, Henry, Bihari and Ou-Yang inequalities

Presents numerous inequalities, which cannot be found in other books

Volume I:

This book focuses on one- and multi-dimensional linear integral and discrete Gronwall-Bellman type inequalities. It provides a useful collection and systematic presentation of known and new results, as well as many applications to differential (ODE and PDE), difference, and integral equations. With this work the author fills a gap in the literature on inequalities, offering an ideal source for researchers in these topics.

The present volume is part 1 of the author’s two-volume work on inequalities.

Integral and discrete inequalities are a very important tool in classical analysis and play a crucial role in establishing the well-posedness of the related equations, i.e., differential, difference and integral equations.

Table of contents (8 chapters)

Linear One-Dimensional Continuous Integral Inequalities
Pages 1-143
Linear One-Dimensional Discrete (Difference) Inequalities
Pages 145-259
Linear One-Dimensional Discontinuous Integral Inequalities
Pages 261-374
Applications of Linear One-Dimensional Inequalities
Pages 375-447
Linear Multi-Dimensional Continuous Integral Inequalities
Pages 449-726
Linear Multi-Dimensional Discrete (Difference) Inequalities
Pages 727-815
Linear Multi-Dimensional Discontinuous Integral Inequalities
Pages 817-888
Applications of Linear Multi-Dimensional Integral and Difference Inequalities
Pages 889-960

Volume II:

This book concentrates on one- and multi-dimensional nonlinear integral and discrete Gronwall-Bellman type inequalities. It complements the author’s book on linear inequalities and serves as an essential tool for researchers interested in differential (ODE and PDE), difference, and integral equations.

The present volume is part 2 of the author’s two-volume work on inequalities.

Integral and discrete inequalities are a very important tool in classical analysis and play a crucial role in establishing the well-posedness of the related equations, i.e., differential, difference and integral equations.

Table of contents (8 chapters)

Nonlinear One-Dimensional Continuous Integral Inequalities
Pages 1-232
Nonlinear One-Dimensional Discrete (Difference) Inequalities
Pages 233-343
Nonlinear One-Dimensional Discontinuous Integral Inequalities
Pages 345-422
Applications of Nonlinear One-Dimensional Continuous, Discontinuous Integral Inequalities and Discrete Inequalities
Pages 423-534
Nonlinear Multi-Dimensional Continuous Integral Inequalities
Pages 535-764
Nonlinear Multi-Dimensional Discrete (Difference) Inequalities
Pages 765-883
Nonlinear Multi-Dimensional Discontinuous Inequalities
Pages 885-988
Applications of Nonlinear Multi-Dimensional Continuous, Discontinuous Integral Inequalities and Discrete Inequalities
Pages 989-1041