Integral and Discrete Inequalities and Their Applications

1. Front Matter

   Pages i-xvi

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2. Nonlinear One-Dimensional Continuous Integral Inequalities

   • Yuming Qin

   Pages 1-232

3. Nonlinear One-Dimensional Discrete (Difference) Inequalities

   • Yuming Qin

   Pages 233-343

4. Nonlinear One-Dimensional Discontinuous Integral Inequalities

   • Yuming Qin

   Pages 345-422

5. Applications of Nonlinear One-Dimensional Continuous, Discontinuous Integral Inequalities and Discrete Inequalities

   • Yuming Qin

   Pages 423-534

6. Nonlinear Multi-Dimensional Continuous Integral Inequalities

   • Yuming Qin

   Pages 535-764

7. Nonlinear Multi-Dimensional Discrete (Difference) Inequalities

   • Yuming Qin

   Pages 765-883

8. Nonlinear Multi-Dimensional Discontinuous Inequalities

   • Yuming Qin

   Pages 885-988

9. Applications of Nonlinear Multi-Dimensional Continuous, Discontinuous Integral Inequalities and Discrete Inequalities

   • Yuming Qin

   Pages 989-1041

10. Back Matter

    Pages 1043-1072

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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.

• nonlinear one-dimensional continuous integral inequalities
• nonlinear one-dimensional discrete inequalities
• nonlinear one-dimensional discontinuous integral inequalities
• nonlinear multi-dimensional continuous integral inequalities
• nonlinear multi-dimensional discrete inequalities
• nonlinear multi-dimensional discontinuous integral inequalities
• Bihari inequality
• ordinary differential equations
• partial differential equations

“The present research book is a useful exposition of mathematical works done by the authors, scattered in many papers over the past decades, involving subjects of classical analysis such as integral inequalities and discrete inequalities. … This book provides a useful collection and systematic presentation of known and new results on nonlinear inequalities, as well as many applications to differential, difference and integral equations. This book is useful for researchers working on these topics.” (Choonkil Park, zbMATH 1377.26021, 2018)

• Department of Applied Mathematics, Donghua University Department of Applied Mathematics, Shanghai, China

  Yuming Qin

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