Abstract
On oscillatory second-order nonlinear delay differential equations of neutral type
Highlights
T his article is concerned with sufficient conditions for oscillation of a nonlinear neutral second-order delay differential equation d d dt r(t) dt z(t) + q(t)G x(t − σ1) + v(t)H x(t − σ2) = 0, t ≥ t0, (1)where z(t) = x(t) + p(t)x(t − τ) and p ∈ PC([t0, ∞), R)
Li et al [2] obtained sufficient conditions for oscillation of solution of second order nonlinear neutral differential equations of the form d r(t) d x(t) + p(t)x(t − τ) γ + q(t) f x(t), x(σ(t)) = 0, dt dt where p, q, r ∈ C([t0, +∞), (0, +∞)) and γ ≥ 1 is the quotient of two odd positive integers
Sufficient conditions are obtained for existence of bounded positive solutions of (3)
Summary
His article is concerned with sufficient conditions for oscillation of a nonlinear neutral second-order delay differential equation d d dt r(t) dt z(t) + q(t)G x(t − σ1) + v(t)H x(t − σ2) = 0, t ≥ t0, (1) Li et al [2] obtained sufficient conditions for oscillation of solution of second order nonlinear neutral differential equations of the form d r(t) d x(t) + p(t)x(t − τ) γ + q(t) f x(t), x(σ(t)) = 0, dt dt where p, q, r ∈ C([t0, +∞), (0, +∞)) and γ ≥ 1 is the quotient of two odd positive integers. Sufficient conditions are obtained for existence of bounded positive solutions of (3).
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