BTC works as a decentralized digital currency because people all over the world verify transactions in exchange for being awarded new bitcoins.  This is known as mining.

Bitcoin creation is capped at 21million bitcoins.  What I do not understand is, why would anyone dedicate computing power to verifying transactions if they will not be awarded bitcoins in exchange for doing so?

It seems to me that once the creation process of bitcoin has ended that the network will cease to function in a way that has currently made it so appealing.

Am I missing something here?  I am excited about bitcoin but less so if it will cease to be useful in a little over 100 years.