The phrase "the basic problem of" is grammatically correct and can be used in written English.
It is typically used when discussing a fundamental or underlying issue or challenge. Example: "The basic problem of poverty is the lack of access to education and job opportunities."
Justice Scalia confirms the basic problem of the appearance of partiality.
The basic problem of Millennium People is that the middle-class revolution idea is so weak.
The basic problem of the calculus was to investigate relations among fluents and their fluxions.
So the basic problem of what to do about Africa remains, despite the administration's determination to get more involved.
But critics say the association's plans would do little to solve the basic problem of access to care.
Hitler denied that science could solve the basic problem of nutrition, but assumed that technology could win territory.
Paul Krugman's optimistic assessment of the chances for universal health care after the Senate's vote on Medicare on Wednesday didn't mention the basic problem of cost control.
Keynes believed that the basic problem of capitalism is not so much its vulnerability to periodic saturations of investment as its likely failure to recover from them.
The TakeTV from SanDisk, for example, uses flash technology to solve the basic problem of moving videos from the computer to the television without running cables across the house or setting up a wireless-video system.
But the basic problem of this lifestyle, as she agrees, is that while there is always someone there for the children, they don't see that much of both parents at the same time.
The basic problem of Shankara's philosophy is how such pure consciousness appears, in ordinary experience, to be individualized ("my consciousness") and to be of an object ("consciousness of blue").
