Is there a way to make a method which is not abstract but must be overridden?

There is no direct compiler-enforced way to do this, as far as I know.

You could work around it by not making the parent class instantiable, but instead providing a factory method that creates an instance of some (possible private) subclass that has the default implementation:

public abstract class Base {
  public static Base create() {
    return new DefaultBase();
  }

  public abstract void frobnicate();

  static class DefaultBase extends Base {
    public void frobnicate() {
      // default frobnication implementation
    }
  }
}

You can't write new Base() now, but you can do Base.create() to get the default implementation.