- #1
mathmari
Gold Member
MHB
- 5,049
- 7
Hey!
I have the following exercise and I need some help..
$"\text{The eigenvalue problem } Ly=(py')'+qy=λy, a \leq x \leq b \text{ is of the form Sturm-Liouville if it satisfies the boundary conditions } p(a)W(u(a),v^*(a))=p(b)W(u(b),v^*(b)). \text{ Show that the boundary conditions of the form: }$
$$ \begin{pmatrix}
y(b)\\
y'(b)
\end{pmatrix}=S\begin{pmatrix}
y(a)\\
y'(a)
\end{pmatrix}, S=\begin{pmatrix}
A & B\\
C & D
\end{pmatrix} $$
$\text{ lead to an eigenvalue problem of the form Sturm-Liouville if } detS=\frac{p(a)}{p(b)}."$
Could you give a hint what to do?
I have the following exercise and I need some help..
$"\text{The eigenvalue problem } Ly=(py')'+qy=λy, a \leq x \leq b \text{ is of the form Sturm-Liouville if it satisfies the boundary conditions } p(a)W(u(a),v^*(a))=p(b)W(u(b),v^*(b)). \text{ Show that the boundary conditions of the form: }$
$$ \begin{pmatrix}
y(b)\\
y'(b)
\end{pmatrix}=S\begin{pmatrix}
y(a)\\
y'(a)
\end{pmatrix}, S=\begin{pmatrix}
A & B\\
C & D
\end{pmatrix} $$
$\text{ lead to an eigenvalue problem of the form Sturm-Liouville if } detS=\frac{p(a)}{p(b)}."$
Could you give a hint what to do?