Oscillation and Nonoscillation of Nonlinear Nonhomogeneous Differential Equations of Third Order

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 5 in Theory of Third-Order Differential Equations, 2014, pp 305-334 from Springer

Abstract: Abstract This chapter is concerned with the study of oscillatory and asymptotic behaviour of nonoscillatory solutions of nonhomogeneous third-order differential equations of the form $$x^{\prime\prime\prime} + a(t) x^{\prime\prime} + b(t)x^{\prime} + c(t) x = f \bigl(t,x,x^{\prime},x^{\prime\prime}\bigr), $$ where a, b and c∈C([σ,∞),R) and f:[σ,∞)×R 3→R, σ∈R. z-type oscillation criteria has been used in this chapter to study the nonoscillation of solutions of the considered equation. As an application, some sufficient conditions have been given for the nonoscillation of different mathematical models in Engineering.

Keywords: Nonoscillatory Solution; Third-order Differential Equation; Asymptotic Behavior; Non-oscillatory Behavior; Singular Solutions (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_5

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DOI: 10.1007/978-81-322-1614-8_5

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