Necessary and sufficient conditions for the nonoscillation of a first order neutral equation with several delays

Rok, strany: 2003, 59 - 70

In this paper, necessary and sufficient conditions have been obtained so that every solution of Neutral Delay Differential Equation (NDDE)

$$ \biggl(y(t)-∑\limits_{j = 1}^k p_j y({t - τ_j})\biggr)' + Q(t)G(y({t-σ})) = f(t) $$

is oscillatory or tends to zero as $t\to∞$ for different ranges of $∑\limits_{j = 1}^k p_j $. This paper improves and generalizes two recent works [DAS, P.—MISRA, N.: A necessary and sufficient condition for the solution of a functional differential equation to be oscillatory or tend to zero, J. Math. Anal. Appl. 204 (1997), 78–87] and [Parhi, N.—Rath, R. N.: On oscillation criteria for a forced neutral differential equation, Bull. Inst. Math. Acad. Sinica 28 (2000), 59–70]. The results of this paper hold for linear, sublinear and superlinear equations. Also, it holds for homogeneous equations. The results can be extended to NDDE with variable coefficients with out assumption of any further condition on the coefficient functions.

ISO 690:

Rath, R. 2003. Necessary and sufficient conditions for the nonoscillation of a first order neutral equation with several delays. In Mathematica Slovaca, vol. 53, no.1, pp. 59-70. 0139-9918.

APA:

Rath, R. (2003). Necessary and sufficient conditions for the nonoscillation of a first order neutral equation with several delays. Mathematica Slovaca, 53(1), 59-70. 0139-9918.