For a Sturm-Liouville problem with a monotone weight that stays positive, all eigenvalues depend on the potential in a uniformly Lipschitz way in the L1 norm.
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Uniform local Lipschitz continuity of eigenvalues with respect to the potential in $L^1[a,b]$
For a Sturm-Liouville problem with a monotone weight that stays positive, all eigenvalues depend on the potential in a uniformly Lipschitz way in the L1 norm.