On a converse of Sturm's comparison theorem

Autor:	Mingarelli, Angelo B.
Rok vydání:	2022
Předmět:	Mathematics - Classical Analysis and ODEs 34C10 34B24 47B50
Druh dokumentu:	Working Paper
Popis:	We show that Sturm's classical comparison theorem (SCT) on the interlacing of zeros of solutions of pairs of real second order two-term ordinary differential equations necessarily fails if the usual Sturmian-type conditions on the coefficients are violated. We also show that the conditions on the coefficients are, in some sense, best possible. We give a necessary and sufficient condition for the failure of SCT and we note that its converse is false, and that the comparison theorem may still hold with very mild hypotheses on the coefficients. Comment: Submitted, 2022
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2204.12457 Zobrazit plný text záznamu View this record from Arxiv