How to Determine if Android Device Supports Live Wallpapers

public static final String FEATURE_LIVE_WALLPAPER was added in API level 7
Feature for getSystemAvailableFeatures() and hasSystemFeature(String).
The device supports live wallpapers.
Constant Value: "android.software.live_wallpaper"

1. Get a PackageManager Instance and save to myPackageManager.

2. Create a Boolean Variable named bolLWSupported

3. Set the Minimum and Target SDK version  to or greater. 

4. In the onCreate method, add the below code. This will return the live wallpapers ability to a boolean named bolLWSupported. It will then display a toast displaying the live wallpapers ability on the device to the user.

bolLWSupported = myPackageManager.hasSystemFeature(PackageManager.FEATURE_LIVE_WALLPAPER);
if (bolLWSupported) {
Toast.makeText(this, "Device supports live wallpapers", Toast.LENGTH_LONG).show();
} else {
Toast.makeText(this, "No live wallpapers support!", Toast.LENGTH_LONG).show();
}

5. Compile and run!

Resources:
http://developer.android.com/reference/android/content/pm/PackageManager.html#FEATURE_LIVE_WALLPAPER