IPhone 5s broke down

Last week on a business trip to the US happened:

In the middle of working it went to blue screen, did not react anymore. Pressing home and start button same time restarted, but shut down again. happened several times, once it was there again could backup a last time. That happened throughout the week, was able to work with the phone sometime, but most of the time it was broke down. Then after 3 days nothing else happened anymore, but the Apple logo for 10 seconds and the black screen again. Complete breakdown.

Somebody else knows about this problems with iPhones?

Peer