Let A1 denote the first eigenvalue of Q"(x) + Ax^20p(x) = 0, p(a) = (b) = 0 for some a, b > 0. Show that the nonlinear problem p"(x) + Ax^2p(x) - p(x)^3 = 0, p(a) = (b) = 0 (1) has only the zero solution provided that = A1.