Consider the problem x2 y = (xy y), y(1) = 0, y(2) = 0. Note that appears as a
Chapter 11, Problem 24(choose chapter or problem)
Consider the problem x2 y = (xy y), y(1) = 0, y(2) = 0. Note that appears as a coefficient of y as well as of y itself. It is possible to extend the definition of self-adjointness to this type of problem and to show that this particular problem is not self-adjoint. Show that the problem has eigenvalues but that none of them is real. This illustrates that in general nonself-adjoint problems may have eigenvalues that are not real.
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