Necessary and Sufficient Condition for Oscillatory and Asymptotic Behaviour of Second-Order Functional Differential Equations
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Authors: S. S. SANTRA
DOI: 10.46793/KgJMat2003.459S
Abstract:
In this paper, necessary and sufficient conditions are obtained for oscillatory and asymptotic behaviour of solutions of second-order neutral delay differential equations of the form
![[ ]
-d- -d-
r(t) [x (t) + p (t)x(τ (t))] + q (t)G (x (σ (t))) = 0, for t ≥ t0,
dt dt](6e9e6f8ee36231f61f6f6f6032a9c7140x.png) |
under the assumption ∫
∞
dη = ∞ for various ranges of the bounded
neutral coefficient p. Our main tools are Lebesgue’s dominated convergence
theorem and Banach’s contraction mapping principle. Further, an
illustrative example showing the applicability of the new results is
included.
Keywords:
Oscillation, nonoscillation, neutral, delay, nonlinear, Lebesgue’s dominated convergence theorem, Banach’s contraction mapping principle.
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