Consider the problem y + y = 0, y(0) + y (0) = 0, y(1) = 0, where is a given constant
Chapter 11, Problem 22(choose chapter or problem)
Consider the problem y + y = 0, y(0) + y (0) = 0, y(1) = 0, where is a given constant. (a) Show that for all values of there is an infinite sequence of positive eigenvalues. (b) If < 1, show that all (real) eigenvalues are positive. Show that the smallest eigenvalue approaches zero as approaches 1 from below. (c) Show that = 0 is an eigenvalue only if = 1. (d) If > 1, show that there is exactly one negative eigenvalue and that this eigenvalue decreases as increases.
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