Oscillation criteria for a generalized Emden-Fowler dynamic equation on time scales

Abstract

In this paper, we consider the second-order Emden-Fowler neutral delay dynamic equationon time scales, where z(t) = x(t) + p(t)x(τ (t)) and β ≥ α > 0 are constants. By means of the Riccati transformation and inequality technique, some oscillation criteria are established, which extend and improve some known results in the literature.

Oscillation and asymptotic properties of a class of second-order Emden–Fowler neutral differential equations

“…Shi et al. (2016) extended the results of Liu et al. (2012) to dynamic equations on time scales provided that and .…”

“…(2012), Shi et al. (2016) are established in the case where . In the hypothesis , there is another parameter and the condition on function f in Li et al.…”

“…(2012) and Shi et al. (2016) also can not apply to (29) and (30) because which does not satisfy the assumptions in Liu et al. (2012), Shi et al.…”

“…(2012), Shi et al. (2016), Baculíková and Džurina (2011), Bohner and Li (2014), Yang et al. (2006), Xu and Meng (2006, 2007).…”

Oscillation results for a fractional order dynamic equation on time scales with conformable fractional derivative

“…Since then, the theory of time scale has received a lot of attention in recent years, and various investigations have been done by many authors [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. Among these investigations, some authors have taken research in oscillation of dynamic equations on time scales (see [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46] and the references therein). In these investigations for oscillation of dynamic equations on time scales, we notice that most of the results are concerned with dynamic equations involving derivatives of integer order, while none attention has been paid to the research into oscillation of fractional order dynamic equations on time scales so far in the literature.…”