Abstract
We analyze the oscillatory behavior of solutions to a class of second-order nonlinear neutral delay differential equations. Our theorems improve a number of related results reported in the literature.
Highlights
In this paper, we study the oscillatory behavior of a class of second-order nonlinear neutral delay differential equations (r(t)z(t)α−1z(t)) + q (t) f (x (σ (t))) = 0, (1)where t ∈ I := [t0, ∞), t0 > 0, z(t) := x(t) + p(t)x(τ(t)), and α > 0 is a constant
We analyze the oscillatory behavior of solutions to a class of second-order nonlinear neutral delay differential equations
We study the oscillatory behavior of a class of second-order nonlinear neutral delay differential equations (r(t)z(t)α−1z(t)) + q (t) f (x (σ (t))) = 0, (1)
Summary
We analyze the oscillatory behavior of solutions to a class of second-order nonlinear neutral delay differential equations. We study the oscillatory behavior of a class of second-order nonlinear neutral delay differential equations (r(t)z(t)α−1z(t)) + q (t) f (x (σ (t))) = 0, (1) We assume that the following conditions hold: (A1) r, p, q ∈ C(I, R), r(t) > 0, p(t) ≥ 0, q(t) ≥ 0, and q(t) is not identically zero for large t; (A2) f ∈ C(R, R), uf(u) > 0, for all u ≠ 0, and there exists a positive constant k such that f (u) |u|α−1u
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