Computational Methods and Function Theory 10 (2010), No. 1, 111--133
Copyright Heldermann Verlag 2010
Kwang C. Shin
kshin@westga.edu , University of West Georgia, Department of Mathematics, Carrollton, GA, U.S.A.
We study the eigenvalues of the non-self-adjoint problem -y''+V(x)y=E y on the half-line 0≤ x<+∞ under the Robin boundary condition at x=0, where V is a monic polynomial of degree at least 3. We obtain a Bohr-Sommerfeld-like asymptotic formula for En that depends on the boundary conditions. Consequently, we solve certain inverse spectral problems, recovering the potential V and boundary condition from the first (m+2) terms of the asymptotic formula.
Keywords: Non-self-adjoint Schrödinger operators, Robin boundary condition, asymptotics of eigenvalues.
MSC 2000: 34L20, 34L40.
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