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Oscillation of Nonlinear Neutral Delay Differential Equations

Elabbasy, E. M.;  Hassan, T. S. — 2008

Serdica Mathematical Journal

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.

Oscillation Criteria for Nonlinear Differential Equations of Second Order with Damping Term

Elabbasy, E. M.;  Elhaddad, W. W. — 2008

Serdica Mathematical Journal

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.

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