Sidon sets in a union of intervals

We study the maximum size of Sidon sets in unions of integers intervals. If $A\subseteq \mathbb{N}$ is the union of two intervals and if $\left| A \right|=n$(where$\left| A \right|$denotesthecardinalityof$A$), we prove that $A$ contains a Sidon set of size at least $0,876\sqrt{n}$. On the other hand, by using the small differences technique, we establish a bound of the maximum size of Sidon sets in the union of $k$ intervals.