Behaviour of Solutions of Linear Homogeneous 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 2 in Theory of Third-Order Differential Equations, 2014, pp 45-146 from Springer

Abstract: Abstract This chapter is concerned with the oscillation and nonoscillation of solutions and their asymptotic behaviour of the linear homogeneous equation with variable coefficients of the form $$x^{\prime\prime\prime}+a(t)x^{\prime\prime}+b(t)x^{\prime}+c(t)x=0, $$ where a,b∈C 1([σ,∞),R) and c∈C([σ,∞),R). Many interesting and nontrivial results are given on the oscillation of solutions of the equation in the following six different cases: (i) a(t)≥0, b(t)≤0, c(t)>0, (ii) a(t)≤0, b(t)≤0, c(t)>0, (iii) a(t)≤0, b(t)≤0, c(t) 0, and (vi) a(t)≤0, b(t)≥0, c(t)

Keywords: Kneser Solution; Nonoscillatory Solution; Third-order Linear Differential Equation; Oscillatory Solutions; Explicit Sufficient Conditions (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_2

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DOI: 10.1007/978-81-322-1614-8_2

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