Uniqueness for Near-Constant Data in Fourth-Order Inverse Eigenvalue Problems1

Let L p u = d4u/dx4 − d/dx p1 du/dx + p2u u 0 = u 0 = u 1 = u 1 = 0 where p ∈ L2 0 1 × L2 0 1 .W e show that for near constant coefficients, if p is even about 1/2 and L p and L ˜p have the same eigenvalues, then knowledge of the first coefficient uniquely determines the second up to average value.F urther, we show that knowledge of the second coefficient uniquely determines the first.W e derive precise eigenfunction asymptotics using resolvent perturbation theory and prove the result using a simple perturbation of basis argument.