The phrase "great difficulties in" is correct and usable in written English.
You can use this phrase to describe a situation where someone is facing a lot of hardship or difficulty. For example, "The charity faced great difficulties in raising the necessary funds."
Even firms in established industries such as energy report facing great difficulties in raising capital.
The painting of skies did not come easy to Constable, who acknowledged "great difficulties" in getting them right.
But aid groups report great difficulties in moving medicine and other supplies through the West Bank and Gaza Strip.
Thus, in writing about early Rome, ancient historians were confronted with great difficulties in ascertaining the truth.
To be the child of families with great difficulties in relationships, with substance abuse or other matters, is far too normal.
The writer of the letter said the Islamic guerrillas had encountered great difficulties in cultivating popular support among the Iraqi people.
"Women who have lost their jobs or who were not working due to external factors now face great difficulties in reentering the market," she noted.
It was concluded that Neolithic men and their ground flint axes had no great difficulties in making large clearings in the forest for the purposes of cultivation.
The rescue operation swiftly turned to one of recovery, and continued through the night as emergency services had great difficulties in extracting remains from the burnt out plane.
The emergence of Trinitarian speculations in early church theology led to great difficulties in the article about the "person" of the Holy Spirit.
Crossair was already facing great difficulties in rebuilding passenger confidence after Swissair's abrupt collapse last month, which stranded nearly 40,000 passengers worldwide for two days while the airline begged its banks for cash to operate.
