Yes, this is an offence under Information Technology Act 2000. If you have recieved SMS with threatening behaviour to kill you etc, then ou should go to your local Cyber Cell and make a formal complaint. Please save all your SMS and data by backing it up on a PC system as Police may want to keep your phone for evidence in case they 'lose it'
Look at the links attached for further information.
I am not a Lawyer, nor do i profess to be one - i just dislike injustice, bullying and corruption.
Change your phone too.
Peace and love to you.