Save a PDF on iOS

Save a PDF from Safari: Apple Support Communities:

• Download a PDF reading app,  like iBooks (free) 
• When your PDF is displayed in Safari you can tap on the document and you'll have an option to "Open in ..." the PDF program. 
• When it opens in iBooks, for example, it also saves a copy of the PDF on the bookshelf so that it is available without needing to go back to the website.

Open PDFs in other apps - Chrome Help

• Touch a PDF link to open the file in Chrome.
• Once the file is open, touch the screen to see an Open in button.
• Touch Open in to see other apps that you can use to open the PDF.