You can switch to a supported J2SE version by editing the asenv file as described here.
If you have not already done so, install the new J2SE version on your system.
The J2SE SDK can be downloaded from http://java.sun.com/j2se/
Stop the Application Server.
Edit the install_dir/config/asenv.conf file (asenv.bat on Windows), changing the value for AS_JAVA to point to the new Java home directory:
Edit the as-install/samples/common.properties file, changing the line beginning com.sun.aas.javaRoot... to reference the new Java home directory.
Restart the Application Server.