偶数阶自共轭微分算子谱的离散性条件

The conditions for the discreteness of the spectrum of self-adjoint differential operators of even order

In this paper, we consider differential operators of 2nd-order
au]=(-1)^k(a_k(x)u^(k)(x))(k), x∈(0, ∞)
whose coefficients a_k(x) are restricted by powers of e^x, and give conditions on the coefficients sufficient to ensure that the spectrum is discrete; next we formulate necessary and sufficient conditions for the discreteness of the spectrum of differential operators whose coefficients a_k(x) may increase as e^αkx as x→∞.