Complex oscillations of non-definite Sturm-Liouville problems, II

Abstract

We correct and update a result of R.G.D. Richardson [13] dealing with the separation of zeros of the real and imaginary parts of non-real eigenfunctions of non-definite Sturm-Liouville eigenvalue problems. We then extend it to the case where the weight function is allowed to be identically zero on a subinterval that excludes the end-points and study the behavior of the zeros of the real and imaginary parts when the end-points are included. Examples are given illustrating the sharpness of the results along with open questions.

20 pages, 5 figures. Typos corrected, Added Lemma4 and Lemma 5 and its corollary and simplified the proofs of many results while omitting others as they are a consequence of the results herein