Oscillation of Solutions of Linear 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 3 in Theory of Third-Order Differential Equations, 2014, pp 147-191 from Springer

Abstract: Abstract Linear nonhomogeneous differential equations of the form 3.1 $$ x^{\prime\prime\prime}+a(t)x^{\prime\prime}+b(t)x^{\prime}+c(t)x=f(t), $$ 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.

Keywords: Nonhomogeneous Linear Differential Equation; Oscillatory Solutions; Nonoscillatory Solution; Non-oscillatory Behavior; Suitable Green's Function (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-81-322-1614-8_3

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