1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Problem with Sturm-Liouville equation

  1. Oct 31, 2006 #1
    Hi there :rofl: .
    I'm having troubles at a point in one Sturm-Liouville problem :grumpy: .

    I am trying to convert a generation eqn to the form of a Sturm-Liouville equation. The equation's form is as follows (where a(x),b(x),c(x),d(x) are arbitrary functions):

    a(x)y'' + b(x)y'(x) + [c(x) + (LAMBDA)d(x)]y(x) = o

    I begin by formatting in y'' + ... form. How do I proceed from here, please?


  2. jcsd
  3. Oct 31, 2006 #2
    If b(x) = a'(x) your equation is in Sturm-Liouville form...
  4. Nov 1, 2006 #3


    User Avatar
    Staff Emeritus
    Science Advisor

    If not, then you need to multiply by some [itex]\mu(x)[/itex] so that it is:
    a(x)[itex]\mu(x)[/itex]y'' + b(x)[itex]\mu(x)[/itex]y'(x) + [c(x) + ([itex]\lambda(x)[/itex])d(x)][itex]\mu(x)[/itex]y(x) = 0

    With a'[itex]\mu(x)[/itex]+ a[itex]\mu'(x)[/itex]= b(x)[itex]\mu(x)[/itex]. That gives you a simple differential equation for [itex]\mu(x)[/itex].
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Problem with Sturm-Liouville equation