select
t.id_article
from
t
inner join (select id_article from t group by id_article having COUNT(1) = 1) t2
on t.id_article = t2.id_article
where
ID_USER = 15
Для правильного вопроса надо знать половину ответа
SELECT `t1`.`id_article`
FROM `table` AS `t1`
LEFT JOIN `table` AS `t2`
ON `t2`.`id_article` = `t1`.`id_article`
AND `t2`.`id_user` != `t1`.`id_user`
WHERE `t1`.`id_user` = :user
AND `t2`.`id_user` IS NULL