It sounds like you have a directory "www.example.com" under public_html/. That's wrong. Your phpBB3 code could be loaded directly into public_html/. For example, the main entry point would be public_html/index.php. What are you using to upload your files?

Note that this structure (loading phpBB3 directly into the root) is OK only if you will never  have anything else on your site. If you will in the future have other stuff (store, gallery, etc.) I would suggest putting phpBB3 into public_html/forum/ and (for the time being) redirecting visitors from the root to this directory. This structure puts applications into their own trees, where they won't step on each other, and permits your own Home Page in the root, with links to the applications.

I erased the other folder with the previous installation.
I have made the installation again straight into public_html.
when i type    www.mydomain.com    it appears the lunarpages' page
when i type    www.mydomain.com/index.html    it appears the lunarpages' page
but
when i type    www.mydomain.com/index.php    it appears my forum. 

I want to appears my forum when i type www.mydomain.com
what can i do?

Thank you, MrPhil for your advices . . . 

P.S. I erase cache and I deleted index.html  and it's ok now. thanks again