How to start dealing with this recurrence relation

Question

I have never seen a recurrence in this form, so I don't know how to proceed. I'm supposed to find asymptotic bounds (preferably $\Theta$(something)) for:

$$T(n) =T\bigg(\frac{n}{\log n}\bigg)+ \log \log n$$

Can you help?

Answer 1

Let $T(n)=U(\log n)$, then $U(\log n)=U(\log n-\log\log n)+\log\log n$.
Let $V(x)=U(x)-x$, then $V(\log n)=V(\log n-\log\log n)=\text{ constant}$