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- Title
NON-OSCILLATORY BEHAVIOUR OF HIGHER ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE.
- Authors
Rath, Radhanath; Misra, Niyati; Mishra, Prayag Prasad; Padhy, Laxmi Narayan
- Abstract
In this paper, we obtain sufficient conditions so that the neutral functional differential equation [r(t)[y(t) - p(t)y(_(t))]'](n-1) + q(t)G(y(h(t))) = |f(t) has a bounded and positive solution. Here n ≥ 2; q, r, h are continuous functions with q(t) ≥ 0; h(t) and r (t) are increasing functions which are less than t, and approach infinity as t → ∞. In our work, r(t) ≡ 1 is admissible, and neither we assume that G is non-decreasing, that xG(x) > 0 for x ≠ 0, nor that G is Lipschitzian. Hence the results of this paper generalize many results in [1] and [4]-[8].
- Subjects
OSCILLATION theory of functional differential equations; ASYMPTOTIC theory in functional differential equations; CONTINUOUS functions; DELAY differential equations; MATHEMATICAL functions
- Publication
Electronic Journal of Differential Equations, 2007, Vol 2007, p1
- ISSN
1550-6150
- Publication type
Article