The phrase "a basic problem that" is correct and usable in written English.
It can be used when introducing a fundamental issue or challenge that needs to be addressed or discussed.
Example: "There is a basic problem that affects the efficiency of our workflow, and we need to find a solution."
Alternatives: "a fundamental issue that" or "a primary concern that".
But underlying it is a basic problem that will only intensify unless we recognize it and try to remedy it.
Amidst all the apparent contradiction and confusion, there is a basic problem that besets all communication between the religious and the secular worlds.
A mathematician called Shinichi Mochizuki may have solved a basic problem that has baffled his peers for decades.
However, a basic problem that arise is how under any possible graph representation, one can be sure that the system is undoubtedly stable.
Existing methods dealing with the time cost trade-off problem, which is encountered in project planning, have focused on the solution of a basic problem that does not adequately represent actual engineering projects.
Therefore, robustness has become an important research topic in control theory, and it is also a basic problem that must be considered in the design of almost all kinds of control systems, such as image and signal processing, combinatorial optimization problems, pattern recognition, etc.
But all the sound and fury about Enron, whose collapse has led to Congressional hearings and media outrage, obscures a more basic problem that is ubiquitous in corporate life today: organizational structures that discourage honesty and suppress truth.
The basic problem that makes it a harder call is that lawyers and judges are by training and habit incrementalists, while information and communications technology moves too fast for incrementalism to keep up.
The most basic problem that leads to a contradictory class definition is the disjointness of physical objects, functions and processes.
However, avoiding sequences prone to deletion does not itself overcome the basic problem that design elements may impose a fitness cost.
Hart's version of legal positivism eschewed transcendental arguments but took seriously the same basic problem that animated Kelsen's theory of law.
