We consider an eigenvalue problem for differential operators, and show how guaranteed bounds for eigenvalues (together with eigenvectors) are obtained and how non-existence of eigenvalues in a concrete region can be assured. Some examples for several types of operators will be presented.
"Numerical Verification Method for Infinite Dimensional Eigenvalue Problems." Japan J. Indust. Appl. Math. 26 (2-3) 477 - 491, October 2009.