Push with my own server

Yes, but you'll need to use a service so that it polls the server every xx minutes when using other apps.

Thank you.

But then I could use SMS as well, or what is the advantage of push service?

A Push Notification is a free service of google (GCM).
With this service you can receive notifications on any data that interests you. I've used it to receive commands from a server to open a particular application, to vibrate the phone, save messages to a file, etc.
I've done it with a servicemodule whith the property # StartAtBoot: True, so that when you reboot the device, start the service again.
To my knowledge, there is no need to scan. It works by intents.
The advantage is that it is a free service from Google, at least for now.

You can see this tutorial link:
http://http://www.b4x.com/forum/basic4android-getting-started-tutorials/19226-android-push-notification-gcm-framework-tutorial.html

Greetings.

Thqank you, I unsderstand it now much better.