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Oscillation and Nonoscillation of Homogeneous Third-Order Nonlinear Differential Equations

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Theory of Third-Order Differential Equations

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Abstract

This chapter deals with third-order linear and nonlinear homogeneous differential equations of the form

$$x^{\prime\prime\prime} + a(t)x^{\prime\prime} + b(t)x^{\prime} + c(t) x^\alpha = 0 $$

and

$$x^{\prime\prime\prime} + a(t)x^{\prime\prime} + b(t)x^{\prime} + c(t) f(x) = 0 $$

where a, b and c∈C([σ,∞),R), α>0 is a ratio of odd integers, f∈C(R,R) such that \(\frac{f(x)}{x} \geq\beta >0\) for x≠0. The necessary and sufficient conditions have been given in terms of the coefficient functions for the oscillation and nonoscillation of solutions of the considered equations for the following cases: (i) a(t)≥0, b(t)≤0 and c(t)>0; and (ii) a(t)≤0, b(t)≤0 and c(t)>0.

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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). Oscillation and Nonoscillation of Homogeneous Third-Order Nonlinear Differential Equations. In: Theory of Third-Order Differential Equations. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1614-8_4

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