'may encounter difficulty' is correct and usable in written English.
You can use it when someone is trying to express that they may experience a problem or obstacle in their efforts. For example: "I may encounter difficulty mastering this new technique."
In using the largest replacement possible, the surgeon may encounter difficulty with closure of the aortotomy.
"Buildings were purchased on the upside, Now, landlords may encounter difficulty justifying rents, and they recognize that there may be a drop.
Kirstjen Nielsen, the homeland security secretary, said in a statement that she had asked volunteers to add more support at the border, and suggested that American citizens may encounter difficulty getting through as a result.
The more elaborate your investment philosophy, the more likely you may encounter difficulty developing a process that works for you.
For a complex problem with huge searching space, this method may encounter difficulty in finding the optimal solution and risk of divergence.
If participants have long eyelashes or narrow eyes, GazeParser may encounter difficulty in pupil detection, as with other video-based eyetrackers, and, therefore, narrow the tracking range.
Current techniques may encounter difficulties to correctly identify the modal parameters.
Should oil and copper prices collapse, Angola, Gabon, Congo, and Zambia may encounter difficulties in servicing their sovereign bonds.
Profit-sharing has proven benefits in terms of increased productivity, but a firm that stands out by offering profit-sharing may encounter difficulties in recruitment among wary workers.
The physicist may encounter difficulties in trying to define death in terms of entropy change and the second law of thermodynamics.
Ignoring for a moment the fact that some older adults may encounter difficulties using smartphones, reminder apps are at least two behavioral steps disconnected from medication intake.
