Problem (F'97, #5). a) Prove that all eigenvalues of the Sturm-Liouville problem d du (player) + Au(x) = 0, + \0, 0 < x

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Problem F 97 5 A Prove That All Eigenvalues Of The Sturm Liouville Problem D Du Player Au X 0 0 0 X 1 (34.5 KiB) Viewed 38 times

Problem (F'97, #5). a) Prove that all eigenvalues of the Sturm-Liouville problem d du (player) + Au(x) = 0, + \0, 0 < x <a, dx du(a) u(0) = 0, + hu(a) = 0, dx are positive. Here h > 0, p(x) > 0 and continuous on (0, a]. b) Show that the same is true when h < 0 and h| is sufficiently small.