Is someone DDOS'ing my minecraft server?

Today I launched my minecraft server and promoted it on some websites. Few players joined and started playing. Suddenly someone joins, says 'Goodbye' and the server is gone. I restart the server, reconnect, and it's down again. And so on…

It's not a cracked server. We're playing with premium accounts.
Is there a way to stop this (plugins/configs/dns/…) and/or get the player who did this banned?

Find a way to change your IP address on your router or talk to your ISP and see if they can help you

banning the player will not fix the problem