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On oscillation of solutions of forced nonlinear neutral differential equations of higher order II

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Parhi N., Rath R.

Annales Polonici Mathematici

2003

tom 81

nr 2

101-110

Sufficient conditions are obtained so that every solution of $[y(t) - p(t)y(t-τ)]^{(n)} + Q(t)G(y(t-σ)) = f(t)$ where n ≥ 2, p,f ∈ C([0,∞),ℝ), Q ∈ C([0,∞),[0,∞)), G ∈ C(ℝ,ℝ), τ > 0 and σ ≥ 0, oscillates or tends to zero as $t→ ∞ $. Various ranges of p(t) are considered. In order to accommodate sublinear cases, it is assumed that $∫_0^{∞} Q(t)dt = ∞$. Through examples it is shown that if the condition on Q is weakened, then there are sublinear equations whose solutions tend to ±∞ as t → ∞.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Parhi N.

1 Rath R.

1 2003

Wyniki wyszukiwania

On oscillation of solutions of forced nonlinear neutral differential equations of higher order II