The eigenvalue ratio of the vibrating strings with mixed boundary condition
Mengze Gu, Hongli Sun · Mathematical Methods in the Applied Sciences · 2023
We provide the lower bound for the ratio of the first two eigenvalues for vibrating strings with the mixed boundary condition, where the density is single‐barrier defined in and the transition point is 0. Moreover, the minimal ratio of the first two eigenvalues is attained by the constant.