Integral and Discrete Inequalities and Their Applications

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.

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

Autorentext

Yuming Qin, born in 1963, is a professor in the School of Mathematics and Statistics and the Institute for Nonlinear Sciences of Donghua University. His research interests are nonlinear evolutionary partial differential equations and their infinite dimensional dynamical systems. He finished more than 30 grants and is currently carrying out four grants from the National Natural Science Foundation of China, Ministry of Science and Technology of China and from the Shanghai Municipal Commission of Science and Technology. Prof. Qin is presently on the editorial boards of 4 international journals and has published over 120 mathematical articles, among which more than 100 articles are indexed in SCI. Prof. Qin has also published 10 monographs since 2008. Xiaolei Dong, born in 1991, is a lecturer in the School of Mathematics and Statistics of Zhoukou Normal University. His research interests are well-posedness of the boundary layer equations. He is currently carrying out one grant from the Natural Science Foundation of Henan Province. Xiuqing Wang, born in 1990, is a lecturer in the School of Faculty of Science of Kunming University of Science and Technology. Her research interests are well-posedness of the boundary layer equations and liquid crystal equations. She is currently carrying out one grant from the Natural Science Foundation of Yunnan Province.

Inhalt
Preface.- Linear One-Dimensional Continuous Integral Inequalities.- Linear One-Dimensional Discrete (Difference) Inequalities.- Linear One-Dimensional Discontinuous Integral Inequalities.- Applications of Linear One-Dimensional Inequalities.- Linear Multi-Dimensional Continuous Integral Inequalities.- Linear Multi-Dimensional Discrete (Difference) Inequalities.- Linear Multi-Dimensional Discontinuous Integral Inequalities.- Applications of Linear Multi-Dimensional Integral and Difference Inequalities.