Time Delay
float delay = 1; // seconds
Timer.schedule(new Task(){
@Override
public void run() {
// Do your work
}
}, delay);
The above code helps you delay the execution, and after that delay you can perform the action you want.
Here, Inside the run method you can switch to any screen and ofcourse you can use this function as many times as you want.
Fitting the image to the screen
batch.draw(texture,0,0,Gdx.graphics.getWidth(),Gdx.graphics.getHeight());
solved How can I create a SplashScreen in LibGDX that goes through 3 images before showing the main menu? [closed]