Consider the eigenvalue problem d2 dx2 + = 0 subject to (0) = 0 and () 2 d dx(0) = 0
Chapter 5, Problem 5.8.7(choose chapter or problem)
Consider the eigenvalue problem d2 dx2 + = 0 subject to (0) = 0 and () 2 d dx(0) = 0. (a) Show that usually 0 u d2v dx2 v d2u dx2 dx = 0 for any two functions u and v satisfying these homogeneous boundary conditions. (b) Determine all positive eigenvalues. (c) Determine all negative eigenvalues. (d) Is = 0 an eigenvalue? (e) Is it possible that there are other eigenvalues besides those determined in parts (b)(d)? Briefly explain.
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