I feel 'I have problems sleeping' looks wrong and it should be 'I have sleeping problems'. But I saw the structure many times in news. What is the difference between them?
Having sleeping problems is long-term, having problems sleeping is short-term.
Here is how I would use each of these terms, with an example.
Sleeping problems : "I have had sleeping problems since I am 7, because every little noise wakes me up."
Problems sleeping : "I have had problems sleeping this week, because there was a lot of noise in the street during the nights."
I think the two constructions are correct depending on the intended meaning. "I have problems sleeping"appears to be addressing disruptive events preceding sleep (not even being able to sleep off) while "I have sleeping problems"appears to be talking to disruptive events that take place while sleeping such as nightmares. This is my take. Thank you.