Abstract
A new method is presented for calculating the critical lengths of linear two-point boundary value problems. The technique is based on solving a nonlinear initial value problem whose solution determines the critical lengths as the zeros of one of the components. In principle the procedure is analogous to the Fredholm factorization of the resolvent kernel in the theory of integral equations. For systems of dimension 2 it is shown the equations are equivalent to a linear system. Numerical results are given establishing the feasibility of the method.
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