I know exactly what I would like to research within my field, however, the ideas are too specific and indeed one of my feedbacks for the reject of one of my PhD applications based on my personal statement was that the university did not have the staff researching my interests.
My friend told me that being too specific, I limit my opportunities. On the other hand, being more general I would risk that I would have to research what the supervisors tell me to and therefore postpone solving the question I am interested in.
What are general strategies for finding appropriate places for studying PhD for someone who has a specific research problem one would like to solve? I am afraid that I may face a similar problem later when searching for a postdoc or an academic place in some research group.