Theory of third-order differential equations [electronic resource] /
Padhi, Seshadev.author.
Pati, Smita.author.
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.
Description based upon print version of record.
Includes bibliographical references and index.
Preface -- Chapter 1: Introduction -- Chapter 2: Behaviour of Solutions of Linear Homogeneous Differential Equations of Third Order -- Chapter 3: Oscillation of Solutions of Linear Nonhomogeneous Differential Equations of Third Order -- Chapter 4: Oscillation and Nonoscillation of Homogeneous Third-order Nonlinear Differential Equations -- Chapter 5: Oscillation and Nonoscillation of Nonlinear Nonhomogeneous Differential Equations of Third Order -- Chapter 6: Oscillatory and Asymptotic Behavior of Solutions of Third Order Delay Differential Equations -- Chapter 7: Stability of Third Order Differential Equations -- References.
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.
Differential equations.
Mathematical analysis.
Calculus.
Difference equations.
Functional equations.
Algebra.
Ordinary Differential Equations.
Analysis.
Difference and Functional Equations.
Algebra.