The lower bounds of the spacings b-a or a’-a of two consecutive zeros or three consecutive zeros of solutions of third order differential equations of the form y”’ + q(t)y’ + p(t)y = 0 (*) are derived under very general assumptions on p and q. These results are then used to show that or as n → ∞ under suitable assumptions on p and q, where ⟨tₙ⟩ is a sequence of zeros of an oscillatory solution of (*). The Opial-type inequalities are used to derive lower bounds of the spacings d-a or b-d for a solution y(t) of (*) with y(a) = 0 = y’(a), y’(c) = 0 and y”(d) = 0 where d ∈ (a,c) or y’(c) = 0, y(b) = 0 = y’(b) and y”(d) = 0 where d ∈ (c,b).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap77-1-3,
author = {N. Parhi and S. Panigrahi},
title = {On distance between zeros of solutions of third order differential equations},
journal = {Annales Polonici Mathematici},
volume = {77},
year = {2001},
pages = {21-38},
zbl = {0989.34023},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap77-1-3}
}
N. Parhi; S. Panigrahi. On distance between zeros of solutions of third order differential equations. Annales Polonici Mathematici, Tome 77 (2001) pp. 21-38. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap77-1-3/