Missouri S&T math professors publish two new books

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The Rolla Building, which houses Missouri S&T’s mathematics and statistics department. Photo by Tom Wagner/Missouri S&T.

Two researchers from Missouri University of Science and Technology have recently published new books focusing on advanced topics in mathematics. 

Dr. Martin Bohner, Curators’ Distinguished Professor of mathematics and statistics, is a co-author of the book Lyapunov Inequalities and Applications. Dr. Vy Le, professor of mathematics and statistics, is a co-author of the book Multi-Valued Variational Inequalities and Inclusions. Both books are published by Springer.

Bohner’s book compiles much of the currently available research on problems called Lyapunov-type inequalities. The book, which includes recent developments on the topic and its relationships to differential equations, is targeted towards senior undergraduate students and graduate students of mathematics and statistics, engineering, and science. 

“These inequalities have been the subject of mathematics research for many years since Aleksandr Lyapunov first discovered the inequality for second-order linear differential equations around the start of the 20th century,” says Bohner. “Since then, far more than 5,000 works have been published on the subject in many different settings. Hence, there was a need to organize this material into a more unified textbook.” 

Le’s book focuses on a class of problems called multi-valued variational differential inequalities. The book aims to provide a systematic description of existence, comparison and enclosure principles in this area of mathematics, as well as explain these problems with other qualitative inequality properties. The book also examines these problems in different function spaces.

“I believe this book is the first in-depth treatise on these problems, and it reflects the current work being done in this part of the theory of partial differential equations,” says Le. “We chose what is included in the book and how it is organized specifically to make it useful and accessible to a broad audience consisting of graduate students and researchers in various areas of mathematical analysis and theoretical physics.”