In your StateBasedGame, in your main method, you can call lwjgl's Display object,
Display.setResizable(true);
This will allow you to resize/maximize the Display window. Make sure you have a recent version of lwjgl!
If you would like to resize the window and make sure the graphics object refreshes it size, you should call this in your update method:
if(Display.getWidth() != container.getWidth() || Display.getHeight() != container.getHeight()) {
try {
app.setDisplayMode(Display.getWidth(), Display.getHeight(), false);
app.reinit();
} catch(Exception e) {
e.printStackTrace();
}
}
And app is your AppGameContainer class. If you are doing gamestates, you can send a reference to the state when it is initialized. If not, you can make a global reference to your container so you can use this snippet of code anywhere in the class.