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The sentence 'problems are increasing' is correct and usable in written English.
You can use this sentence when referring to an increase in the amount of problems one is facing. For example, "The number of problems I have to deal with are increasing, and I'm not sure how to handle them."
Exact(17)
"Day by day, our problems are increasing," Mr. Khan said.
Drug abuse and associated health-related problems are increasing.
Children are spending more time indoors while pediatric mental and behavioral health problems are increasing.
But, the authors note, it is not clear if the sleep problems are increasing the risk of developing the disease or vice versa.
This is the first annual report of its kind, so it's hard to gauge whether mental health problems are increasing among women, or whether we're getting better at seeking diagnoses and help.
Beyond the toll on exports, Europe's problems are increasing volatility in the stock market, exacerbating the skittishness of American consumers and generating additional uncertainty for American firms about the pace of global economic growth.
Similar(43)
If unrecognized, the risks of failed knee surgery to correct these problems are increased [3].
Corrosion, the load on fluid handling facilities, and environmental problems are increased by increasing the amount of unwanted water production.
At the same time, reports of problems were increasing.
The application of these methods to solve bi-objective production optimization problems is increasing.
Certainly, there is reason to believe that the number of people seeking support for mental health problems is increasing all over.
More suggestions(2)
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com