THE DIFFERENCE OF CONSECUTIVE EIGENVALUES

Authors
KU HT KU MC
Citation
Ht. Ku et Mc. Ku, THE DIFFERENCE OF CONSECUTIVE EIGENVALUES, Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics, 57, 1994, pp. 305-315
Citations number
6
Categorie Soggetti
Mathematics, General","Statistic & Probability",Mathematics,"Statistic & Probability
Journal title
Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics → ACNP
ISSN journal
02636115
Volume
57
Year of publication
1994
Part
3
Pages
305 - 315
Database
ISI
SICI code
0263-6115(1994)57:<305:TDOCE>2.0.ZU;2-P
Abstract
Let M be a smooth bounded domain in R(n) with smooth boundary, n great er-than-or-equal-to 2, and DELTAu = - SIGMA(i=1)n partial derivative2u /partial derivativex(i)2. We prove an inequality involving the first k + 1 eigenvalues of the eigenvalue problem: [GRAPHICS] where a(m-1) gr eater-than-or-equal-to 0 are constants and a(t-1) = 1. We also obtain a uniform estimate of the upper bound of the ratios of consecutive eig envalues.