A convergence theorem on a measure chain (Q2747455)

The authors prove a Kamke-type theorem for dynamic equations on a measure chain (time scale) \({\mathbb T}\). This theorem states that, under certain assumptions, a sequence \(\{y_n(t)\}_{n=1}^\infty\) of solutions to the first-order dynamic equation \(y^\Delta=f(t,y)\) has a uniformly convergent (on compact subintervals of \({\mathbb T}\)) subsequence \(\{y_{n_k}(t)\}_{k=1}^\infty\). Moreover, this subsequence converges to a solution \(y_0(t)\), which satisfies the limiting initial condition of \(y_n\) as \(n\to\infty\).