how can i make the results of a google search form staying at my url?
usualy, the forms directs to google.com, but look here: http://www.illustrated-db-discography.nl/ (jump to section: search): at this site the results actualy stays at the same url! and its not just a google page with some cosmetics as in http://blogs.salon.com/0001111/stories/2002/09/30/finetuningCustomGoogleSear.html

There are two searches that can be done, the web itself, or the site. If you search the web, the results appear on a google page framed by the site.

There are two searches that can be done, the web itself, or the site. If you search the web, the results appear on a google page framed by the site.

o.k. and how do i frame it? what is the code?

There is no simple "code". HTML Frames have been around for years, since the very early days. I suggest you start with the official documentation, and as you write your code and hit difficulties, come back to ask specific questions.