Search results both in sidebar and content part

Hi! I have a question regarding search results. I want to have the standard Wordpress search showing the results in the sidebar. I have two versions of my site, one in 801+ pixels, and one in 800 and down. On the smaller version I want the usual search function, but when having a sidebar I would like to get both the results in the sidebar and the specific page/post displayed on the content part. I would also like the search results to be permanent, even in the event of a click on another link. See the picture: for an example.

Now, what is the easiest way to do this?