The phrase "a major problem facing" is correct and usable in written English.
You can use it to describe a significant issue that is currently being encountered or dealt with by a person, group, or society.
Example: "Climate change is a major problem facing our planet today, affecting ecosystems and human livelihoods."
Alternatives: "a significant challenge confronting" or "a critical issue impacting".
This is a major problem facing America.
But commentators suggest this is a major problem facing the mining industry.
A major problem facing Japan is deflation, or a general decline in prices because of a lack of demand.
A major problem facing the endurance program was that the contemporary variant of the now-venerable Soyuz was limited to a two-month stay in space; beyond this time, its propellant system would deteriorate.
But Ms. Weingarten and many teachers at the rally asserted that the city's demands would make life harder for teachers and would aggravate a major problem facing city schools: attracting the thousands of certified teachers it needs.
If a respondent mentions narcotics addiction as a major problem facing the country, for instance, this answer might be coded as a health problem or a crime problem, or it might be grouped with other replies dealing with drug abuse or alcoholism.
A major problem faced by both agencies is that Islamic radicals determined to inflict harm on America are not likely to volunteer their services to American intelligence.
A major problem faced by small voluntary organisations is finding the time and resources for back office administration, and partnerships can add to that workload rather than alleviate it.
Autoimmune disorders of the skin are a major problem, faced by 1 3% of the population worldwide.
A major problem faced in biomedical informatics involves how best to present information retrieval results.
Solid precipitation from crude oils is a major problem faced by the petroleum industry during depletion from reservoirs.
