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Oscillation of Solutions of Linear Nonhomogeneous Differential Equations of Third Order

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Theory of Third-Order Differential Equations

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Abstract

Linear nonhomogeneous differential equations of the form

$$ x^{\prime\prime\prime}+a(t)x^{\prime\prime}+b(t)x^{\prime}+c(t)x=f(t), $$
(3.1)

where a,b∈C 1([σ,∞),R) and c∈C([σ,∞),R), has been considered in Chap. 3. Existence of oscillatory solutions of the equation has been given in this chapter for the cases (i) a(t)≥0, b(t)≤0, c(t)>0, (ii) a(t)≤0, b(t)≤0, c(t)>0, and (iii) a(t)≥0, b(t)≥0, c(t)>0. Rest cases have been left as an open problem. Further, Green’s function method has been given in this chapter so that all oscillatory solutions of a linear nonhomogeneous differential equation of the form (7.65) tends to zero eventually.

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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 of Solutions of Linear Nonhomogeneous 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_3

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