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It may be worth a quick email to Google if you wish to use a free search engine on your site, and add Google ads to the results pages. I would imagine some free search engines [ for integration into a website] may have some spyware in them, but Gogle will set you straight on the subject, and clarify if it's OK.
It's maybe worth a look:
You can restrict the search to just your site and link the AdSense earnings to your account. You can also boost URLs that match specific patterns so pages you think are of more value to your users are likely to be further up (maximum of 5,000 patterns).
Either way the sites must be indexed by G properly, or it won't work.
In my experience the income, when linked to your Adsense account, from the ads is about the same as for G site search. Big difference the flexibility you get when using G coop.
I run a site search service. It does not make sense to display ads on the results pages because the ads will not be targetted to the content of the search results page.
That's correct for advertising that's contextual and not aware of the search string.
Running a Google CSE means Google serves advers based on the search phrase, this means the ads should be very relevant.
If you take the approach of running a site search with in conjunction with an XML feed for your adverts then you can also ensure the ads are as relevant as possible (limited by the relevance that the service that you rely on can get anyway). An example of this is using something like Sphinx for your site search and serving Overture adverts which are fetched based on the search string.
Running adverts on your own site search is not always the best option, but it can be helpful to users when you have few/no matching results so why not run the sites search and then decide whether to show the adverts based on the number (and relevance of site results).