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?

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

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