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given the generalized SL conditions

Let's say psi_m and psi_n are eigenfunctions of the given y.

Its Wronskian is 0 because otherwise the boundary condition doesn't make sense much.

However, I wonder if it is possible to have,

S={ x | W[psi_m(x) , psi_n(x)] =/= 0 }

otherwise W[psi_m(x) , psi_n(x)] = 0

then alpha and alpha' are 0 at such points, but still satisfies SL conditions.

Would it matter because at those points we can have any psi_m(x) and psi_n(x)?

If not could anyone tell me why?

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# I Sturm-Liouville Problem, boundary condition

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