Oscillation of third order nonlinear functional dynamic equations on time scales (Q609442)

The purpose of the paper is to give oscillation criteria for the third order nonlinear functional dynamic equation \[ (a(t)[(r(t)x^{\Delta}(t))^{\Delta}]^{\gamma})^\Delta+f(t,x(g(t)))=0 \] on a time scale \(\mathbb{T}\), where \(\gamma\) is a quotient of odd positive integers, \(a\) and \(r\) are positive rd-continuous functions on \(\mathbb{T}\), and the function \(g:\mathbb{T}\to\mathbb{T}\) satisfies \(\lim_{t\to\infty}g(t)=\infty\) and \(f\in C(\mathbb{T}\times\mathbb{R},\mathbb{R})\). Some examples are given to illustrate the main results.