Abstract:
For the spectrum of the operator
$$u=\sum_{j=1}^n{(-1)^{m_j}D_j^{2m_j}u+q(x)u},$$
to be discrete, where the mj are arbitrary positive integers such that $\sum_{j=1}^n{\frac1{2m_j}<1}$, and $q(x)\ge 1$, it is necessary and sufficient that $\int\limits_K{q(x)dx\to\infty}$ , when the cube $K$ tends to infinity while preserving its dimensions.
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