is it possible to use jquery ajax to send GET variables to Solr and update the content page so the user doesnt have to reload the page?
Jquery – solr with jquery ajax
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Your question is a bit strange, as "Yes it most surely is possible" would be the answer.
You don't provide any additional information on what you tried already, why I didn't work out for you and so on. You also didn't provide any info on your "webpage environment" which platform, which languages generate the site, how is the connection so solr made .....
Now aside with all this: Already from the startpage of Apache Solr you can easily conclude that it should be (even easily) possible to use ajax to make the search requests.
There is a json api. Sounds perfect for ajax uses.
The Apache Solr wiki even explains how this could work out
AJAX Solr (it actually is js-framework agnostic but already comes with a jQuery compatible manager)