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We establish some new criteria for the oscillation of the even order neutral dynamic equation a(t) (x(t) − p(t)x(τ (t))) ∆ n−1 α ∆ + q(t) (x σ (g(t))) λ = 0 on a time scale T, where n ≥ 2 is even, α and λ are ratios of odd positive integers, a, p and q are real valued positive rd-continuous functions defined on T, and g and τ are real valued rd-continuous(More)
In this paper, Oscillatory and asymptotic behaviour of solutions of a class of nonlinear fourth order neutral differential equations with positive and negative coefficients of the form (H) (r(t)(y(t) + p(t)y(t − τ))) + q(t)G(y(t − α)) − h(t)H(y(t − β)) = 0 and (NH) (r(t)(y(t) + p(t)y(t − τ))) + q(t)G(y(t − α)) − h(t)H(y(t − β)) = f (t) are studied under the(More)
In this paper, lower bounds for the spacing (b − a) of the zeros of the solutions and the zeros of the derivative of the solutions of third order differential equations of the form y + q(t)y + p(t)y = 0 (*) are derived under the some assumptions on p and q. The concept of disfocality is introduced for third order differential equations (*). This helps to(More)
In this paper, oscillatory and asymptotic properties of solutions of nonlinear second order neutral dynamic equations of the form r(t)(y(t) + p(t)y(α(t))) Δ Δ + q(t)G(y(β (t))) − h(t)H(y(γ(t))) = 0 and r(t)(y(t) + p(t)y(α(t))) Δ Δ + q(t)G(y(β (t))) − h(t)H(y(γ(t))) = f (t) are studied under assumptions ∞ 0 1 r(t) Δt < ∞ and ∞ 0 1 r(t) Δt = ∞ for various(More)
In this paper, oscillatory and asymptotic behaviour of solutions of a class of nonlinear fourth order neutral differential equations with several delay of the form (r(t)(y(t) + p(t)y(t − τ))) + m i=1 q i (t)G(y(t − α i)) = 0 and (E) (r(t)(y(t) + p(t)y(t − τ))) + m i=1 q i (t)G(y(t − α i)) = f (t) are studied under the assumption ∞ 0 t r(t) dt = ∞ for(More)
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