Existence of periodic solutions for higher order dynamic equations on time scales (Q1936101)

The author studies a sufficient condition for the existence of a periodic solution for the nonlinear \(n\)-th order dynamic equations \[ x^{\Delta^n}=f(x^{\Delta^{n-1}},\dotsc,x^{\Delta},x,t),\;n\geq2 \] on a time scale \(\mathbb{T}\) with period \(\sigma(T)\). He derives necessary a priori bounds based on a Wirtinger-type inequality and proves the main result by using coincidence degree theory.