On the oscillations of the solutions for a class of second order nonlinear functional dynamic equations on time scales with unbounded neutral coefficients (Q6104176)

This paper deals with second order functional dynamic equations of the form \[ \left( l(t)(w^{\Delta }(t))^{\xi }\right) ^{\Delta }+f(t,(xoh)(t))=0,~t\in \lbrack t_{0},\infty )_\mathbb{T}, \] where \(\xi >0\) is a quotient of odd integers, \[ w(t)=x(t)+\sum\limits_{i=1}^{n}p_{i}(t)(xo\eta _{i})(t),~t\in \lbrack t_{0},\infty )_\mathbb{T}. \] Using Riccati transformation technique sufficient conditions for the oscillation of the solutions are obtained. Moreover, two examples are given to illustrate the results.