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Mathematics - Dynamical Systems & Differential Equations | Theory of Third-Order Differential Equations

Theory of Third-Order Differential Equations

Padhi, Seshadev, Pati, Smita

2014, XV, 507 p.

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  • Highlights the results that hold good for constant coefficient equations of third order linear differential equations
  • Contains all the latest results, with the reasons for their importance in the present context
  • Furthers the studies of M. Gregus, who first studied third order linear 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.

Content Level » Research

Keywords » Asymptotic behaviour - Delay differential equations - Nonoscillatory solution - Oscillatory solution - Stability, asymptotic stability

Related subjects » Algebra - Analysis - Dynamical Systems & Differential Equations

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