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I Sturm-Liouville Problem, boundary condition

  1. Mar 28, 2016 #1

    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?
  2. jcsd
  3. Mar 29, 2016 #2
    ah, forgot to mention that, alpha' = alpha_2. whereas alpha = alpha_1

    I could not find the equation picture of SL conditions of wronskian using psi_m, psi_n and alpha and alpha'.
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