Oscillation theorems for linear differential equations of second order

On the Oscillations of Nonlinear Third Order Neutral Differential Equations

“…(E) by using a generalized Riccati transformation and integral averaging technique of Philos-type [12]. Let …”

“…Recently, increasing attention has been devoted to the oscillation of differential equations of the form (E) and some of its exceptions; have been the subject of intensive researchs see for example the papers [1][2][3][4][5][6][7][8][9][10][11][12][13] and references cited in. In particular, we mention here the paper of Grace et al [5] which studied the oscillation of the third order delay differential equation.…”

Oscillation Theorems for a Class of Nonlinear Second Order Differential Equations with Damping

“…Following Philos [10], let us introduce now the class of functions  which will be extensively used in the sequel. Let     …”

Oscillation of certain third-order quasilinear neutral differential equations

“…Following the ideas of Philos [18] and Sun [19], we now establish new Kamenevtype oscillation [19] for Eq. (1.1).…”

“…Then Eq. (1.1) reduces to the following equation 18) where z(t) = x(t)+p(t)x(δ(t)), and functions a(t), δ(t), τ (t), p(t) and q(t) satisfy (H1)-(H3). Then (2.1) becomes …”