Necessary and Sufficient Conditions for Oscillation of Second Order Neutral Differential Equations

By J. Wong. 2000

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Consider the second order nonlinear neutral differential equation with delays: (E) d2/dt2[y(t) − py(t − τ)] + q(t)f(y(t − σ)) = 0, for t ∈ [0, ∞), where q(t), f(x) are continuous functions, q(t) ≥ 0, yf(y) > 0 if y ≠ 0, and 0 0, σ > 0. When f(y) satisfies either the superlinear or sublinear conditions which include the special case f(y) = y|y|γ − 1 of γ > 1 and 0 < γ < 1, respectively, we give necessary and sufficient conditions for the oscillation of all continuable solutions of (E). When p = τ = σ = 0 in (E), these results reduce to the well known theorems of Atkinson and Belohorec in the special case when f(y) = y|y|γ − 1, γ ≠ 1.

Subfields: Applied Mathematics, Numerical Analysis

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