While there isn't an official solution, there are ways to do this.

For example, the site steemwatch.com lets you specify any number of notifications - when a user posts something new, upvotes something, is tagged in a post, etc.
The site watches the blockchain for you and notifies your account whenever an event you've subscribed to happens. As for getting it pushed to your phone, Steemwatch can integrate with your RocketChat (SteemChat) or Slack account. So, when one of these events happens, you get a message on Slack or Steemchat pushed to your phone.

I'm happy to help you set that up if you need any assistance. Others may chime in with different solutions as well.

I don't know if [@good-karma](steemit.com/@good-karma) has built in push notifications for posts on the eSteem mobile app yet, but you could always make that request.