Defining an abstract class without any abstract methods
Solution 1:
Of course.
Declaring a class abstract only means that you don't allow it to be instantiated on its own.
Declaring a method abstract means that subclasses have to provide an implementation for that method.
The two are separate concepts, though obviously you can't have an abstract method in a non-abstract class. You can even have abstract classes with final methods but never the other way around.
Solution 2:
Yes you can do it. Why don't you just try doing that?