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Fourth order Dirichlet bounday value problem

  1. Dec 7, 2005 #1
    Consider the fourth order Dirichlet (biharmonic) boundary value problem

    y^(4) + [ lambda - q(t)] y = 0 in ( 0,1),

    y(0) = y'(0) = 0

    y(1) = y'(1) = 0

    Where q : [0,1] -> R is continuous function. Prove that if phi(t, lambda 1) and phi(t, lambda 2) are solutions of this equation corresponding to distinct values of lambda, i.e., lambda 1 doesn't equal lambda2, then functions phi(t, lambda 1) and phi(t, lambda2) are orthogonal on (0,1).
     
  2. jcsd
  3. Dec 9, 2005 #2
    you must itegrate this eeqution
     
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