iphone 3gs keeps shutting down when using an app or messaging after upgrade to IOS5

Iphone Reset

Reset your phone:

Press the sleep/wake button & home button at the same time, keep pressing until you see the Apple logo, then release the buttons...

The Basic Troubleshooting Steps are:

Restart.. Reset.. Restore from Backup... Restore as New...

Restarting your device

1) Press and hold the Sleep/Wake button for a few seconds until the red "slide to power off" slider appears, and then slide the slider.

2) Press and hold the Sleep/Wake button until the Apple logo appears.

Follow these steps to reset your device

Note: Reset your device only if it is no longer responding and the steps above do not work.

Press and hold the Sleep/Wake button and the Home button together for at least ten seconds, until the Apple logo appears.

iPhone Reset

http://support.apple.com/kb/ht1430

Backing up, Updating and Restoring

http://support.apple.com/kb/HT1414