The phrase "a unique problem in" is correct and usable in written English.
It can be used when discussing a specific issue that is distinct or singular within a particular context or field.
Example: "The researchers identified a unique problem in the data collection process that had not been addressed in previous studies."
Alternatives: "a distinct issue in" or "a singular challenge in".
"New York has a unique problem in terms of health care work-force shortages".
But Nicaraguan officials answer with some bitterness that they face a unique problem in applying an amnesty.
A14 Chinese Tackle Spitting The Chinese government is handing out white plastic bags to tackle a unique problem in its battle against SARS -- spitting, a longstanding Chinese tradition that potentially spreads the disease.
A rare disease presents a unique problem in treatment because the number of patients with the disease is so small (fewer than 200,000 in the United States) that it is not worthwhile for companies to go through the lengthy and expensive process required for approval and marketing.
We have a unique problem in that we've been playing in Bristol for 126 years and I don't think there is enough awareness of that.
Orphan works – works to which the copyright owner cannot be located or identified – present a unique problem, in that achieving free access and use of the works is often impossible.
For a totally new agent, the estimated interval between initial infection and detailed characterization is variable and depends on the presence of unusual symptoms, the failure to identify a virus after using all available specific tests, the recognition of a unique problem, and, in the past, the ability to grow the agent in culture.
A unique problem occurs in evaluating and treating patients with gallstone-induced cholangitis, pancreatitis or biliary obstruction from strictures or tumors.
Parallelism creates a unique problem for achieving reproducibility in Monte Carlo simulations because it changes the order in which values are summed.
"[Social networks like Twitter and Facebook] have a very unique problem, in that all these audiences are very disaggregated.
Gophers and groundhogs present a unique problem, as they burrow tunnels in the ground and eat seeds, roots and often your entire garden bounty.
