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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)

- SAROJ PANIGRAHI, RAKHEE BASU, WANTONG LI, QUAN HONGSHUN
- 2015

In this paper, the authors study oscillatory and asymptotic behavior of solutions of a class of nonlinear higher order neutral differential equations with positive and negative coefficients of the form (a(t)(b(t)(y(t) + p(t)y(σ (t))))) (n−2) + q(t)G(y(α(t))) − h(t)H(y(β (t))) = 0 (E) for n 3 , n is an odd integer, 0 p(t) p 1 < 1 and −1 < p 2 p(t) 0. The… (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, 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)

- Saroj Panigrahi
- 2014

In this paper, we estimate Liapunov-type integral inequalities for a single, cycled, and coupled dynamic system of one-dimensional p-Laplacian problems with weight functions having stronger singularities.

- Saroj Panigrahi, R. Basu
- 2014

In this paper oscillatory and asymptotic behavior of solutions of a class of nonlinear second order neutral differential equations with positive and negative coefficients of the form (r 1 (t)(x(t) + p 1 (t)x(τ (t))) ′) ′ + r 2 (t)(x(t) + p 2 (t)x(σ(t))) ′ +p(t)G(x(α(t))) − q(t)H(x(β(t))) = 0 and (r 1 (t)(x(t) + p 1 (t)x(τ (t))) ′) ′ + r 2 (t)(x(t) + p 2… (More)

- Saroj Panigrahi
- 2013

In this paper, Liapunov-type integral inequalities has been obtained for third order dynamic equations on time scales by using elementary analysis. A criterion for disconjugacy of third order dynamic equation is obtained in an interval [a, σ(b)].

- Saroj Panigrahi, Rakhee Basu
- 2012

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)