Current browse context:
math.CA
Change to browse by:
References & Citations
Mathematics > Classical Analysis and ODEs
Title: On the non-existence of oscillation numbers in Sturm-Liouville theory
(Submitted on 30 Apr 2024)
Abstract: We prove an old conjecture that relates the existence of non-real eigenvalues of Sturm-Liouville Dirichlet problems on a finite interval to the non-existence of oscillation numbers of its real eigenfunctions, [[6], p.104, Problems 3 and 5]. This extends to the general case, a previous result in [1], [2] where it was shown that the presence of even one pair of non-real eigenvalues implies the non-existence of a positive eigenfunction (or ground state). We also provide estimates on the Haupt and Richardson indices and Haupt and Richardson numbers thereby complementing the original Sturm oscillation theorem with the Haupt-Richardson oscillation theorem discovered over 100 years ago with estimates on the missing oscillation numbers of the real eigenfunctions observed.
Submission history
From: Angelo B. Mingarelli Prof. [view email][v1] Tue, 30 Apr 2024 14:09:48 GMT (16kb)
Link back to: arXiv, form interface, contact.