What specifically are the problems you have? Installing issues? Problems getting the launcher to load? Errors during log-in? Disconnecting from the game? Details needed to determine if it's something new or more of the typical issues that PSN has been having since the PS4 launched:

https://downdetector.com/status/playstation-network

The PS4 also has been having specific problems with the latest firmware as well. Tweet from last night:

https://twitter.com/PlayStation/stat...11271476477952
We're aware of issues happening post PS4 2.00 firmware, including some freezes and boot errors. Working to resolve ASAP, will update soon.
So, there could simply be something going on at Sony's end that needs to be addressed.