The phrase "experienced some difficulties" is correct and can be used in written English.
It is often used to describe a situation in which someone faced adversity or had trouble succeeding in a task. For example, "The students had experienced some difficulties with the new material, but eventually grasped the concepts."
Unfortunately, in practice, I experienced some difficulties with the service.
Publishing in Breton experienced some difficulties in the years following World War II.
The service, which reportedly has roughly 700,000 subscribers, has experienced some difficulties – not the least that Jay Z forgets he has a stake in it.
"Erudio has experienced some technical issues with their systems in getting up to date deferment status information, and as a result a small number of customers may have experienced some difficulties.
The HST volunteers also experienced some difficulties.
She experienced some difficulties due to the language barrier.
Sotheby's probably experienced some difficulty in putting together its sale.
The surgery was considered a success, but Way has experienced some difficulty, and he was scheduled to have arthroscopic surgery this month to clean up other problems.
Large eddy simulation (LES) is now widely regarded as an improvement on existing computational fluid dynamics (CFD) techniques in addressing classes of combustion problems where traditional CFD approaches have experienced some difficulty 1, 2, 3.
One participant (5%) understood the question but experienced some difficulty with the response options for this item, saying the question could be improved by collecting a more detailed response on each patient's subjective experience with burning.
The witnesses testified about their interactions with Lody and identified him as the man who had posed as "Charles A. Inglis", though the proprietress of the Edinburgh boarding-house experienced some difficulty.
