Introduction

Seshadev Padhi and Smita Pati
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Seshadev Padhi: Birla Institute of Technology, Mesra, Department of Applied Mathematics
Smita Pati: Birla Institute of Technology, Mesra, Department of Applied Mathematics

Chapter Chapter 1 in Theory of Third-Order Differential Equations, 2014, pp 1-44 from Springer

Abstract: Abstract In this chapter, we consider the third-order linear differential equation with constant coefficients of the form 1.1 $$ x^{\prime\prime\prime}+ax^{\prime\prime}+bx^{\prime}+cx=0,\quad t \geq \sigma, $$ where a, b, and c are real constants. We have considered eight different cases for the constants a, b, and c while studying the structures of spaces of oscillatory and nonoscillatory solutions of (7.5). Further, it is observed that different structures of solution spaces of (7.5) appear for the eight different cases on a, b, and c. Two comparison theorems are also given in this chapter on the oscillation theory of the nonhomogeneous equation 1.2 $$ x^{\prime\prime\prime}+ax^{\prime\prime}+bx^{\prime}+cx=f, $$ where a, b, c, and f are constants. Introductions to third-order delay differential equations and third-order canonical differential equations are also given. The results obtained in this chapter provide some basic ideas on the oscillation and nonoscillation of third-order linear and nonlinear differential equations with variable coefficients.

Keywords: Cauchy Sequence; Delay Differential Equation; Oscillatory Solution; Oscillation Theory; Nonoscillatory Solution (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-81-322-1614-8_1

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DOI: 10.1007/978-81-322-1614-8_1

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