Sharp estimates of lowest positive Neumann eigenvalue for general indefinite Sturm-Liouville problems

Given two measures mu, nu and their total variations, we study the minimization of Neumann eigenvalues for measure differential equation dy(center dot) = y(t)d mu(t) + lambda y d nu (t). By solving the infinitely dimensional minimization problem of the lowest positive Neumann eigenvalue for the measure differential equation, we obtain the optimal lower bound of the lowest positive Neumann eigenvalue for the Sturm-Liouville problem y '' = q (t)y + lambda m(t)y, where q(t) is a nonnegative potential function and the other potential function m(t) admits to change sign.(c) 2023 Elsevier Inc. All rights reserved.