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The present paper shows that the eigenvalue sequence $\{\lambda_n(q)\}_{n\geqslant 1}$ of regular Sturm-Liouville eigenvalue problem with certain monotonic weights is uniformly Lipschitz continuous with respect to the potential $q$ on any bounded subset of $L^1([a,b],\mathbb{R})$.

Uniform local Lipschitz continuity of eigenvalues with respect to the potential in L^1[a,b]