This is what I did recently to generate core dump of Weblogic server running in Solaris box. Had to spend sometime to figure it out where the dump is being generated.
Here are the steps I followed:
ps -ef | grep java command.
 Identify the process id of the Weblogic process [ Make sure only one Weblogic process is running so that it’s easy to identify ].
 Run the command
kill -3 process_id
 Assuming that the Weblogic server is started using
nohup ./startWeblogic.sh & command, the core dump will be appended to nohup.out file.
 You can check this by doing
Shift + F on nohup.out file.