“This monograph is devoted to the qualitative behavior of solutions (oscillation, non-oscillation, stability, asymptotic behaviors, etc.) of various ordinary differential equations of third order with and without delay. It is suitable for those mathematicians and of other sciences dealing with mathematics and engineering. … In summary, this monography is useful for researches investigating the qualitative behavior of solutions of ordinary differential equations of third order.” (Cemil Tunç, zbMATH 1308.34002, 2015)
“This is a comprehensive monograph on third-order differential equations, spanning more than 500 pages and collecting recent results on qualitative behavior of solutions of these equations. … the book may serve as a basis for understanding the oscillatory and asymptotic theory of third-order differential equations, offering a comprehensive account of today’s knowledge in the field and a rich source of references for specialists.” (Zuzana Došlá, Mathematical Reviews, November, 2014)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.
