moreover,

let say myscript.sh is running and having the below process id-

solaris:/home/user1> ps -ef|grep myscript.sh
solaris 25907 10427 0 14:36:50 ? 0:00 /export/home/myscript.sh

i put the myscript.sh in cron as 1 minute interval. So, every 1 minute interval solaris again run the myscript.sh.

DO you think solaris May try to assing the next myscript.sh with procss id 25907( which indicating overlapping)?
procss id 25907 still running.....