Here is the logic that you should follow.
You should get the owner of the post - thread. After logging of an user you should check whether this user is the owner of the post. If it is the owner then show "Mark as Answer" button on the posts. You should create a Boolean type variable to determine whether the post is marked or not. By default the value is false. Once a user click on the button you should set the variable to true and apply a new css to the marked post. Then you rebind the items in the repeater and the new css will became visible.
the Telerik team