Theory of Third-Order Differential Equations

SESHADEV PADHI is associate professor of mathematics at Birla Institute of Technology, Mesra, Ranchi, Jharkhand, India. He received his PhD on the topic "oscillation theory of third-order differential equations". He was awarded the Better Opportunities for Young Scientists in Chosen Areas of Science and Technology (BOYSCAST) fellowship by the Department of Science and Technology (DST), Government of India in 2004, to visit Mississippi State University, USA, where he subsequently did his postdoctoral research. In addition, Dr. Padhi has visited several institutes of international repute: Florida Institute of Technology, Melbourna, Florida, USA, in 2006 to work in collaboration with Prof. T. Gnanabhaskar; Texas State University, San Marcos, Texas, USA, in 2009 to work in collaboration with Prof. Julio G.Dix; University of Tennessee, Chattanooga, Tennessee, USA, in 2011, 2012 and 2013 to work in collaboration with Prof. John R. Graef; University of Szeged, Szeged, Hungary, in 2007 and2011 to work in collaboration with Prof. Tibor Krisztin. Besides, he also visited Eidgenössische Technische Hochschule (ETH) Zürich, Switzerland, under Borel Set Theory Programme in 2005, and many other countries to deliver lectures in international conferences and workshops. Dr. Padhi has published more than 60 research papers in international journals of repute and has been working as referee for Mathematical Review for more than 30 international journals since 2006.

SMITA PATI is a postdoctoral fellow in the Department of Applied Mathematics, Birla Institute of Technology, Mesra, Ranchi, India, working under the postdoctoral grant from the National Board for Higher Mathematics (NBHM), Department of Atomic Energy (DAE), Government of India. Besides, Dr. Pati has been working as a referee for seven international mathematics journals and for Mathematical Review. She was awarded with Marqui's Whos Who in the year 2012 and has published 15 research papers in international journalsof repute, in addition to publishing several research papers in collaboration with Prof. Julio G. Dix, Texas State University, USA, and John R. Graef, University of Tennessee, Chattanooga, Tennessee, USA. She has visited several institutes in Hungary and Italy to deliver lectures in different conferences on Differential Equations.

This book discusses the theory of third-order differential equations. Most of the results are derived from the results obtained for third-order linear homogeneous differential equations with constant coefficients. M. Gregus, in his book written in 1987, only deals with third-order linear differential equations. These findings are old, and new techniques have since been developed and new results obtained.

Chapter 1 introduces the results for oscillation and non-oscillation of solutions of third-order linear differential equations with constant coefficients, and a brief introduction to delay differential equations is given. The oscillation and asymptotic behavior of non-oscillatory solutions of homogeneous third-order linear differential equations with variable coefficients are discussed in Ch. 2. The results are extended to third-order linear non-homogeneous equations in Ch. 3, while Ch. 4 explains the oscillation and non-oscillation results for homogeneous third-order nonlinear differential equations. Chapter 5 deals with the z-type oscillation and non-oscillation of third-order nonlinear and non-homogeneous differential equations. Chapter 6 is devoted to the study of third-order delay differential equations. Chapter 7 explains the stability of solutions of third-order equations. Some knowledge of differential equations, analysis and algebra is desirable, but not essential, in order to study the topic.