# Are all fourth-order self-adjoint differential operators also Sturm Liouville?

Suppose we have a fourth-order differential operator $$L$$ that we know is self-adjoint. Suppose also that the typical Sturmian boundary conditions are satisfied.

Is $$L$$ also Sturm Liouville? (This is true for second-order) That is, can it be put into Sturm Liouville form? If so, does this involve using integrating factors like the second-order analogue and/or is it tougher to do?

• I've never seen Sturm-Liouville refer to anything but second order self-adjoint. – DisintegratingByParts Jan 16 at 17:05