Non-oscillatory criteria for a class of second order non-linear forced neutral-delay differential equations |
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| Authors: | R N Rath N Misra P P Mishra |
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| Institution: | (1) Department of Mathematics, Veer Surendra Sai University of Technology, Burla, 768018, Sambalpur District, Orissa, India;(2) Department of Mathematics, Berhampur University, Berhampur, 760007, Orissa, India;(3) Department of Mathematics, Silicon Institute of Technology, Bhubaneswar, Orissa, India |
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| Abstract: | In this paper, sufficient conditions are obtained, so that the second order neutral delay differential equation has a positive and bounded solution, where q, h, f ∈ C (0, ∞), ℝ) such that q(t) ≥ 0, but ≢ 0, h(t) ≤ t, h(t) → ∞ as t → ∞, r ∈ C
(1) (0, ∞), (0, ∞)), p ∈ C
(2) 0, ∞), ℝ), G ∈ C(ℝ, ℝ) and τ ∈ ℝ+. In our work r(t) ≡ 1 is admissible and neither we assume G is non-decreasing, xG(x) > 0 for x ≠ 0, nor we take G is Lipschitzian. Hence the results of this paper improve many recent results.
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| Keywords: | neutral differential equation oscillation non-oscillation |
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