The phrase "a difficult problem that" is correct and usable in written English.
You can use it when introducing a specific issue or challenge that requires attention or resolution.
Example: "The researchers faced a difficult problem that needed innovative solutions to overcome."
Alternatives: "a challenging issue that" or "a complex situation that".
There remains the important task of persuading patients and physicians to adopt wise counsel, a difficult problem that may turn out to be managed care's true advantage.
Despite intensive researches on medical image segmentation, aneurysm (Lumen, Thrombus, and Parent Blood Vessels) segmentation remains as a difficult problem that has not been yet resolved.
In general, a σ-field need not be all subsets of the sample space S. The question of whether all subsets of [0, 1] are Lebesgue-measurable turns out to be a difficult problem that is intimately connected with the foundations of mathematics and in particular with the axiom of choice.
Although the methods presented here were not fully effective (one subject was consistently recognized under the forced choice study design even at the maximum deformation level employed) this paper may point a way toward solution of a difficult problem that has received little attention in the literature.
Attribution of the tidal spectrum at 110 km to specific sources and propagation conditions at lower altitudes is a difficult problem that remains to be solved.
If your energy "hits the wall" at 2 3pm, that isn't the time to schedule a brainstorming session or work on a difficult problem that requires creativity and focus.
This is a particularly difficult problem that requires an understanding of the consequences of the mutations at the network level, and the capacity to predict the appropriate levels of the network that can be used to counteract them (see above).
Disposal of plutonium and other high-level wastes is a more difficult problem that continues to be a subject of intense debate.
Meanwhile, Eero gets two very talented product people who have already been working on a very difficult problem that gets to the heart of its business.
Hutchins and other squad members involved in the killing, Bouza said, "were trying to solve a complex, difficult problem that went awry".
Adjusting for treatment compliance during follow-up is a very difficult problem that is the subject of ongoing research.
