Try facebook, in this manner: You need to search on the names you believe your half brothers to have. If you get any hits, check the "about" tab just in case they have put any personal info there - most people don't, but occasionally you get a place of birth or school named.
Then check out their "friend" list and search for any familiar surnames. Think not only of their birth surname, but also their mother's maiden name, any names of grandparents or cousins on their mother's side. (You may need to build a small family tree for their mother if you haven't already).
Then look at any photos they've put on. If anyone has "liked" them or commented on them, check the names of those people in case there is anything familiar.
If you're looking at an older generation, you may say -- oh, these people are too old,they won't be on FB - but you might be surprised. It's not uncommon for younger family members to set Granddad up with an account so he can see their photos etc.
if all this fails, it could be that they're not on FB but it could also be that their mother remarried and changed the surname. You may need to check out possible marriages for this.