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2000 Mathematics Subject Classification: 34K15, 34C10.
In this paper, we study the oscillatory behavior of first order nonlinear neutral delay differential equation
(x(t) − q(t) x(t − σ(t))) ′ +f(t,x( t − τ(t))) = 0,
where σ, τ ∈ C([t0,∞),(0,∞)), q О C([t0,∞), [0,∞)) and f ∈ C([t0,∞) ×R,R). The obtained results extended and improve several of the well known previously results in the literature. Our results are illustrated with an example.
2000 Mathematics Subject Classification: 34C10, 34C15.
Some new criteria for the oscillation of all solutions of second order differential equations of the form
(d/dt)(r(t)ψ(x)|dx/dt|α−2(dx/dt))+ p(t)φ(|x|α−2x,r(t) ψ(x)|dx/dt|α−2(dx/dt))+q(t)|x|α−2 x=0,
and the more general equation (d/dt)(r(t)ψ(x)|dx/dt|α−2(dx/dt))+p(t)φ(g(x),r(t) ψ(x)|dx/dt|α−2 (dx/dt))+q(t)g(x)=0,
are established. our results generalize and extend some known oscillation criterain in the literature.
2010 Mathematics Subject Classification: 39A10, 39A12.
2010 Mathematics Subject Classification: 34C10, 34C15.
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