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"have experienced difficulty" is correct and usable in written English.
You can use it to describe a situation where you or someone else has faced a challenge or a problem. For example, "The students have experienced difficulty with understanding equations."
Exact(17)
"I, for one, have experienced difficulty during my formal study years with the best of textbooks around".
"In the past five years, rising numbers of children and their families have experienced difficulty in satisfying their most basic material and educational needs," says the report.
Engineers have experienced difficulty when attempting to use enveloping or high fiducial limit statistical techniques for defining the shock environment by shock spectra.
But for the last year or so, with the contraction of the global economy and the dynamism of Chinese (Xiaomi) and Indian (Micromax) competitors in the smartphone industry, the giant chaebols of South Korea — Samsung first, then Hyundai and a few others — have experienced difficulty.
Reviewers have experienced difficulty categorizing the Popotan anime, though it does feature an overall comedic tone.
However, an April 2014 survey conducted by the MacArthur Foundation tells us that 59percentt of respondents throughout the country have experienced difficulty in finding affordable quality housing options to buy.
Similar(43)
We sincerely apologise to our customers who have experienced difficulties.
In turn, some businesses that depended on council contracts have experienced difficulties themselves.
Even the most knowledgeable relief agencies have experienced difficulties providing sanitation alternatives in such challenging scenarios.
Although many studies of collaboration in engineering education have shown positive effects on performance, some, even those employing technologies, have experienced difficulties.
Historical narratives suggest that people living on the fringes of the Okavango Delta have experienced difficulties over a long period of time.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com