Oscillation criteria for a class of nonlinear differential equations of third order

Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping

“…Compared to second order differential equations, the study of oscillation and asymptotic behaviour of third order differential equations has received considerably less attention in the literature. In the ordinary case for some recent results on third order equations the reader can refer to Bartusek [3], Cecchi and Marini [4,5], Parhi and Das [19][20][21]23,24], Skerlik [32][33][34], Tiryaki and Yaman [38].…”

Oscillation criteria for third order nonlinear delay differential equations with damping

“…It is easy that to check that all hypotheses of Theorem 2.9 are satisfied and hence every solution y of equation (2.24) is oscillatory or y is oscillatory. One such solution is y(t) = sin t. We note that none of the results in [3,8,[10][11][12][13][14][15] are applicable to equation (2.24).…”

“…Compared to second order differential equations, the study of oscillation and asymptotic behavior of third order differential equations has received considerably less attention in the literature. In the ordinary case for some recent results on third order equations the reader can refer to Cecchi and Marini [3,4], Parhi and Das [10,11], Parhi and Padhi [12], Skerlik [13], Tiryaki and Yaman [14], Aktas and Tiryaki [1]. It is interesting to note that there are third order delay differential equations which have only oscillatory solutions or have both oscillatory and nonoscillatory solutions.…”

“…But the corresponding ordinary differential equation y (t) + y(t) = 0, admits a nonoscillatory solution y 1 (t) = e −t and oscillatory solutions y 2 (t) = e t/2 sin √ 3/2t and y 3 (t) = e t/2 cos √ 3/2t . In the literature there are some papers and books, for example Agarwal et al [2], Grace and Lalli [5], Parhi and Das [10,11], Parhi and Padhi [12], Skerlik [13], and Tiryaki and Yaman [14], which deal with the oscillatory and asymptotic behavior of solutions of functional differential equations. In [1,15], the authors used a generalized Riccati transformation and an integral averaging technique for establishing some sufficient conditions which insure that any solution of equation (1.1) oscillates or converges to zero.…”

Nonoscillation and oscillation of solutions of a class of third order difference equations

“…Our method of proof could improve the results of Popenda and Tan and Yang when applied to (2) and (3), respectively. The motivation for our work on third order difference equations is mainly derived from the work on third order differential equations contained in [3,4,[6][7][8][9] and the work on third order difference equations contained in [2]. In Section 2, sufficient conditions are obtained for nonoscillation of all solutions of (1).…”