How does a researcher identify or recognize a problem that is appropriate for doctoral research?
Without being flip about this, this is a case of "you know it when you see it." There is no real objective, quantifiable way to determine what sort of problem or question is worthy of a dissertation.
Here is the general process that I and most of the people I knew in graduate school went through to find a dissertation topic. First, you look for issues that interest you as you take classes early in your graduate career. Once you have found a general area of interest, you start to look at books that have been published in that area. Since a dissertation is a book-length work, that starts to give you a feel for how big a dissertation topic has to be. Finally, you continue to read as much as you can in your area. You try to identify topics that you think are interesting (and the right size) and which have not yet been researched. As you get closer to deciding on a topic, you should have already identified a faculty member who might be able to serve as your dissertation adviser. You need to start talking to that person well before it is time to have your topic. He or she should be able to help you as well.
Unfortunately, there is no easy way to tell whether a topic is going to work as the subject for your dissertation.
Obviously, we can say that it's not a easy task to identify a dissertation topic. You have to fist identify what are your interests and what you know about the topics as a background info. Then you have to make a research on finding out some doctoral work ideas based on your expertise on certain areas. You have to next take a look at those list prepared after research and even short list that to identify what makes a great selection. It's a fact that a successful quality thesis writing is often based on how you work on topic selection. You have to propose the list of interesting subject areas to your mentor and get his advises as well in making a final decision. Never consider the process of topic identification as easy, because it has all importance and even can influence your flow of writing to a great extent.