Can have an abstract class implementing all of its methods-- with no abstract methods in it.
Eg.:
public abstract class someClass
Well assume that you don't care whether the methods of the abstract class are implemented or abstract, but by design it has to be abstract so that when someone extends it, they have to add more methods or override the existing ones or use as is. If they don't want to override the methods then the default behavior is already provided in that abstract class.
In this abstract class, the only criteria you enforce is - one simply cannot instantiate that class and they have to have their only version of class before using it.
So in general, abstract class with few or all methods being implemented, is much better than having an interface which has no methods implemented at all. This is based on the assumption that you are using it as a single inheritance.