The article explores a model of economic growth where the Hamilton-Jacobi-Bellman equation has multiple solutions, but the value function doesn't always satisfy it. The researchers identify that the lack of a solution to the original problem is key to this issue. They show that specific conditions are needed for a solution to exist, and when they are met, the value function is the only nondecreasing concave solution to the equation. However, without these conditions, this uniqueness doesn't hold.