一类四阶对称微分算子的下方无界性

On the Unboundedness below of the Four-order Symmetrical Differential Operator

证明了如果四阶对称微分算式的首项系数在一个正的Lebesgue测度集上是负的,则最小算子(且该对称微分算式的任何自伴实现)是下方无界的.

It is proved that if the leading coefficient in a four-order symmetrical differential expression is negative on a set with positive Lebesgue measure,then the minimal operator (and hence any self-adjoint realization of the four-order symmetrical differential expression) is unbounded below.