Fourth-order Sturm Liouville form
$begingroup$
A fourth-order ODE in the form
begin{align}
[p(x)f''(x)]'' - [q(x)f'(x)]' + s(x) f(x) = lambda r(x) f(x),
end{align}
is in a fourth-order Sturm Liouville form. In the simpler second-order problem, I know that every second-order ODE can be written in the second-order Sturm Liouville form.
Is this true for any fourth-order ODE? Suppose I have
begin{align}
sum_{i=0}^4a_i(x) f^{(i)}(x) = lambda r(x) f(x),
end{align}
is it possible to always write this in the form above?
sturm-liouville
asked Jan 9 at 15:55
K LK L
436
$endgroup$
add a comment |
$begingroup$
A fourth-order ODE in the form
begin{align}
[p(x)f''(x)]'' - [q(x)f'(x)]' + s(x) f(x) = lambda r(x) f(x),
end{align}
is in a fourth-order Sturm Liouville form. In the simpler second-order problem, I know that every second-order ODE can be written in the second-order Sturm Liouville form.
Is this true for any fourth-order ODE? Suppose I have
begin{align}
sum_{i=0}^4a_i(x) f^{(i)}(x) = lambda r(x) f(x),
end{align}
is it possible to always write this in the form above?
sturm-liouville
asked Jan 9 at 15:55
K LK L
436
$endgroup$
add a comment |
$begingroup$
A fourth-order ODE in the form
begin{align}
[p(x)f''(x)]'' - [q(x)f'(x)]' + s(x) f(x) = lambda r(x) f(x),
end{align}
is in a fourth-order Sturm Liouville form. In the simpler second-order problem, I know that every second-order ODE can be written in the second-order Sturm Liouville form.
Is this true for any fourth-order ODE? Suppose I have
begin{align}
sum_{i=0}^4a_i(x) f^{(i)}(x) = lambda r(x) f(x),
end{align}
is it possible to always write this in the form above?
sturm-liouville
asked Jan 9 at 15:55
K LK L
436
$endgroup$
A fourth-order ODE in the form
begin{align}
[p(x)f''(x)]'' - [q(x)f'(x)]' + s(x) f(x) = lambda r(x) f(x),
end{align}
is in a fourth-order Sturm Liouville form. In the simpler second-order problem, I know that every second-order ODE can be written in the second-order Sturm Liouville form.
Is this true for any fourth-order ODE? Suppose I have
begin{align}
sum_{i=0}^4a_i(x) f^{(i)}(x) = lambda r(x) f(x),
end{align}
is it possible to always write this in the form above?
sturm-liouville
sturm-liouville
asked Jan 9 at 15:55
K LK L
436
asked Jan 9 at 15:55
K LK L
436
edited Jan 9 at 16:07
K L
asked Jan 9 at 15:55
K LK L
436
asked Jan 9 at 15:55
K LK L
436
asked Jan 9 at 15:55
K LK L
436
436
add a comment |
add a comment |
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