Mixing
Are all fourth-order self-adjoint differential operators also Sturm Liouville?
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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?
ordinary-differential-equations sturm-liouville
asked Jan 16 at 1:55
K LK L
436
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add a comment |
$begingroup$
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?
ordinary-differential-equations sturm-liouville
asked Jan 16 at 1:55
K LK L
436
$endgroup$
$begingroup$
I've never seen Sturm-Liouville refer to anything but second order self-adjoint.
$endgroup$
– DisintegratingByParts
Jan 16 at 17:05
add a comment |
$begingroup$
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?
ordinary-differential-equations sturm-liouville
asked Jan 16 at 1:55
K LK L
436
$endgroup$
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?
ordinary-differential-equations sturm-liouville
ordinary-differential-equations sturm-liouville
asked Jan 16 at 1:55
K LK L
436
asked Jan 16 at 1:55
K LK L
436
asked Jan 16 at 1:55
K LK L
436
asked Jan 16 at 1:55
K LK L
436
asked Jan 16 at 1:55
K LK L
436
436
$begingroup$
I've never seen Sturm-Liouville refer to anything but second order self-adjoint.
$endgroup$
– DisintegratingByParts
Jan 16 at 17:05
add a comment |
$begingroup$
I've never seen Sturm-Liouville refer to anything but second order self-adjoint.
$endgroup$
– DisintegratingByParts
Jan 16 at 17:05
$begingroup$
I've never seen Sturm-Liouville refer to anything but second order self-adjoint.
$endgroup$
– DisintegratingByParts
Jan 16 at 17:05
$begingroup$
I've never seen Sturm-Liouville refer to anything but second order self-adjoint.
$endgroup$
– DisintegratingByParts
Jan 16 at 17:05
add a comment |
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$begingroup$
I've never seen Sturm-Liouville refer to anything but second order self-adjoint.
$endgroup$
– DisintegratingByParts
Jan 16 at 17:05