searching multiple pdfs

Yes, this is very easy but only after having downloaded them to one folder locally. Assuming you have Adobe Acrobat DC (free) just group the PDF's you want to search in the same folder (wherever takes your fancy) and open them all which will start Adobe Acrobat DC. Then from the menu EDIT | ADVANCED SEARCH or Ctrl -Shift-F and select the radio button "all PDF documents in" and choose the folder you have the PDF documents in. Type or copy paste your search term. You don't have to specifically open every PDF in that folder to search it, but if you open at least one then it will start Adobe DC for you rather than starting it from the menu. (6 and two 3's really). If you have lots of PDF's don't open then all just group in the folder and they will only open when it finds the search term.

Those answers are helpful.  Thank you both.  What I'm really trying to find out is if there is a way to go through a collection of links to PDFs on a site and find every mention of a keyword or name or place, with a link to the specific page within each PDF.  Similar to the functionality in advanced search in Reader that allows you to find every instance of a mention-- in context-- with a direct link.  Is there a tool for that?  Or would google be the best option?

Google will find text that is in a PDF,  filetype:pdf to your search, it will only report search findings that are PDF files.

I hope this is helpful.

My best,

Dave

Yes, it's called Google.