We give sufficient conditions for the unique solvability and maximal regularity of a generalized solution of a second-order differential equation with unbounded diffusion, drift, and potential coefficients. We prove the compactness of the resolvent of the equation and an upper bound for the Kolmogorov widths of the set of solutions. It is assumed that the intermediate coefficient grows quickly and does not depend on the growth of potential. The diffusion coefficient is positive and can grow or disappear near infinity, i.e. the equation under consideration can degenerate. The study of such equation is motivated by applications in stochastic processes and financial mathematics.

我们为具有无界扩散，漂移和势系数的二阶微分方程的广义解的唯一可解性和最大正则性提供了充分条件。我们证明了方程解的紧致性和解集的Kolmogorov宽度的上限。假设中间系数快速增长，并且不依赖于电位的增长。扩散系数为正，并且可以在无穷大附近增长或消失，即所考虑的方程可以退化。对此类方程式的研究是受随机过程和金融数学应用的推动。