The discrete spectrum of a class of differential operators with product of power function and exponential function

Using the method of direct sum decomposition and estimation of the corresponding quadratic forms,the discrete spectrum of a class of 2n-th order differential operators are considered,whose coefficients contain product of power function and exponential function.Some sufficient conditions are given which ensure that the spectrum of differential operators is discrete.And the discreteness of spectrum of some differential operators can be easily judged.