Oscillation criteria for first-order dynamic equations with nonmonotone delays

 In this paper, we consider the first-order dynamic equation as the following: $$x^{\Delta}insert ignore into journalissuearticles values(t);+\sum\limits_{i=1}^m p_iinsert ignore into journalissuearticles values(t);xinsert ignore into journalissuearticles values(\tau_iinsert ignore into journalissuearticles values(t););=0,\,\,t\in[t_0,\infty);_{\mathbb{T}}$$ where $p_{i}\in C_{rd}\leftinsert ignore into journalissuearticles values( [t_{0},\infty );_{\mathbb{T}},\mathbb{R}^{+}\right); ,$ $\tau _{i}\in C_{rd}\leftinsert ignore into journalissuearticles values( [t_{0},\infty );_{\mathbb{T}},\mathbb{T}\right); $ $insert ignore into journalissuearticles values(i=1,2,\ldots ,m);$ and  $\tau_iinsert ignore into journalissuearticles values(t);\leq t,\,\, \lim_{t\to\infty}\tau_iinsert ignore into journalissuearticles values(t);=\infty$.  When the delay terms $\tau_{i}insert ignore into journalissuearticles values(t);$ $insert ignore into journalissuearticles values(i=1,2,\ldots ,m);$ are not necessarily monotone, we present new sufficient conditions for the oscillation of first-order delay dynamic equations on time scales.