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Upper and Lower bound eigenvalues Sturm Liouville problem

  1. Apr 7, 2009 #1
    I have 2 questions that need to be solve:

    01. Find upper and lower bound for the k-th eigenvalue [tex]\lambda_{k}[/tex] of the problem [tex]((1+x^2)u')'-xu+\lambda(1+x^2)u[/tex] for [tex] 0< x< 1 [/tex] with boundary conditions [tex] u(0)=0 [/tex] and [tex] u(1)=0 [/tex]

    02. Find a lower bound for the lowest eigenvalue of the problem
    [tex] ((1+x^2)u')'+\lambda(1+x^2)u=0 [/tex] for [tex] 0 < x < 1 [/tex] with boundary conditions [tex] u(0)=0 [/tex] and [tex] u'(1)=0 [/tex]

    many thanks and looking forward from anyone. please put the steps as well.
     
  2. jcsd
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