We present new oscillation criteria for the second order nonlinear neutral delay differential equation ( a (t) (y (t) + p (t) y (tâˆ’ Ï„))â€² )â€² + q (t) |y (Ïƒ (t))|Î±âˆ’1 y (Ïƒ (t)) = 0, where t â‰¥ t0, Ï„, andâ€¦ (More)

This paper is concerned with oscillation of the second-order halflinear delay dynamic equation (r(t)(x)) + p(t)x(Ï„(t)) = 0, on a time scale T, where Î³ â‰¥ 1 is the quotient of odd positive integers,â€¦ (More)

In this paper, we will establish some sufficient conditions which guarantee that every solution of the third order nonlinear dynamic equation (c(t)(a(t)x(t))) + q(t)f(x(t)) = 0, t â‰¥ t0, oscillates orâ€¦ (More)

The third order linear differential equation Ly = y'" + p2(t)y" + P\{i)y' + Po(')y = 0 is studied, where />,(/) are continuous real-valued and periodic of period <o > 0. Various criteria are obtainedâ€¦ (More)

By means of generalized Riccati transformation techniques and generalized exponential functions, we give some oscillation criteria for the nonlinear dynamic equation (p(t)x âˆ† (t)) âˆ† + q(t)(f â€¢ x Ïƒ) =â€¦ (More)

We present new oscillation criteria for the second order nonlinear damped delay dynamic equation (r(t)(x(t))) + p(t)(x(t)) + q(t)f (x(Ï„(t))) = 0. Our results generalize and improve some known resultsâ€¦ (More)

We consider a linear Hamiltonian Difference System for the so-called singular case so that discrete Sturm]Liouville Equations of higher order are included in our theory. We introduce the concepts ofâ€¦ (More)

In this paper we establish some new oscillation criteria for the third-order nonlinear dynamic equation (c(t) ( (a(t)x(t)) )Î³ ) + f(t, x(t)) = 0, t âˆˆ [a,âˆž)T on time scales, where Î³ â‰¥ 1 is a quotientâ€¦ (More)

We obtain some boundedness and oscillation criteria for solutions to the nonlinear dynamic equation (p(t)x âˆ† (t)) âˆ† + q(t)(f â€¢ x Ïƒ) = 0, on time scales. In particular, no explicit sign assumptionsâ€¦ (More)