Expanding on my comment above, what I mean is you can use a search engine that can index your whole file system and then search for content.
An example of generic search engine I have used in the past is Sphinx Search. It has various plugins for different interfaces. There are others like Apache Solr, Elasticsearch, etc. They all require you to invest some time to undertsand how they work, and getting an interface e.g. a simple web page? If you are considering this route, I suggest also looking at github, as there may be new simpler search engines for Linux.
But to have a more structured search, you need a system like Calibre already suggested by others to import the pdfs...
edit: On Windows 10 for instance, you can index the whole file system by changing settings to also index file contents, under “Indexing Options”. Then you can use the “File Manager” search box to search for any text of interest. I can't remember is something similar exists on Linux, apart from using "find" and "grep" from the command-line.