[6] In 1999, he was a member of the Ukrainian national youth team, which won the Under-16 Chess Olympiad in Artek, Ukraine.

[7] In 2007 Eljanov won the B group of the Corus Chess Tournament in Wijk aan Zee, the Netherlands with a score of 9/13 points.

[10] In the same year, Eljanov played in the GM Rapid event of the Richard Riordan Chess Festival at the 18th Maccabiah Games.

Later that year, in September, he won the 14th Anatoly Karpov International Tournament (pl), a category 18 round-robin event in Poikovsky, Russia.

In 2016, he won the Chess.com Isle of Man International tournament in Douglas edging out Fabiano Caruana on tiebreak after both scored 7½/9 points.