The difference of consecutive eigenvalues
Hsu-Tung Ku, Mei-Chin Ku · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1994
Abstract Let M be a smooth bounded domain in Rn with smooth boundary, n ≥ 2, and . We prove an inequality involving the first k + 1 eigenvalues of the eigenvalue problem: where am−1 ≥ 0 are constants and at−1 = 1. We also obtain a uniform estimate of the upper bound of the ratios of consecutive eigenvalues.