Pfiles
Solaris 10 doesn't come with lsof, and a non-root user can't compile and run lsof. However, the pfiles command in Solaris 10 can offer similar functionality. Unfortunately, it doesn't list all files from all processes, but you can check on a single process.
$ pfiles 4653 | grep "/" | grep -v "/devices/" 4653: /opt/java/jdk1.5.0_14/bin/amd64/java -Djboss.deploy.env=rhubarb /logs/application/serverlog/stdout.200807312021.log /logs/application/serverlog/gc.log /var/run/name_service_door /logs/application/serverlog/prod.log /u/prod/servers/jboss-r/server/20080731/data/hypersonic/localDB.lck /u/prod/servers/jboss-r/server/20080731/data/hypersonic/localDB.log