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Behaviour of Solutions of Linear Homogeneous Differential Equations of Third Order

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Theory of Third-Order Differential Equations

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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, (iv) a(t)≥0, b(t)≤0, c(t)<0, (v) a(t)≥0, b(t)≥0, c(t)>0, and (vi) a(t)≤0, b(t)≥0, c(t)<0. Open problems are incorporated at the end of the chapter for future work.

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Authors and Affiliations

  1. Department of Applied Mathematics, Birla Institute of Technology, Mesra, Ranchi, Jharkhand, India

    Seshadev Padhi & Smita Pati

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  1. Seshadev Padhi
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  2. Smita Pati
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Padhi, S., Pati, S. (2014). Behaviour of Solutions of Linear Homogeneous Differential Equations of Third Order. In: Theory of Third-Order Differential Equations. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1614-8_2

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