The phrase 'there remain problems' is correct and usable in written English.
It can be used whenever you would like to refer to problems that remain after making an effort to solve them. For example: "Despite our best efforts, there remain problems that must still be addressed."
There remain problems to address inside Locke, too.
"There remain problems with consumer awareness and education.
Unfortunately, there remain problems with the generation, the distribution and the storage of hydrogen, as well as with the cost of the fuel cells themselves.
While there remain problems with thinking that these neurons' activity simply constitute any pleasure, or are either necessary or sufficient for all pleasure, they seem at least very closely connected with some pleasure.
There remain problems with activating follow-through investigations for sources in all the four study areas.
Even though there are only four genes catalogued by InSiGHT, there remain problems mapping the gene names, preventing some matches.
Within such a schema there remain problem cases.
"You have, certainly, improvement in the labor market in the U.S. but every once in a while we got reminded there still remain problems in Europe," said Greg Woodard, a portfolio strategist at Manning & Napier in Fairport, N.Y.
The Quality Assurance programme for ER, PR and human epidermal growth factor receptor 2 (HER2) in the UK has to some extent addressed this, but for other biomarkers, including Ki67, there clearly remain problems.
Of course there remain real problems (some of which are discussed above) with the unificationist account of explanation and, for that matter, with the MRL theory of laws[33], but the integrated account that would result from putting the two together nonetheless might be taken to illustrate the sort of thing we should be aiming at.
However there are remaining problems with RP annotation.
