On distance between zeros of solutions of third order differential equations

N. Parhi, and S. Panigrahi. "On distance between zeros of solutions of third order differential equations." Annales Polonici Mathematici 77.1 (2001): 21-38. <http://eudml.org/doc/280745>.

@article{N2001,
abstract = {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 $t_\{n+1\} - tₙ → ∞$ or $t_\{n+2\} - tₙ → ∞$ 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).},
author = {N. Parhi, S. Panigrahi},
journal = {Annales Polonici Mathematici},
keywords = {zeros of solutions; lower bounds of zeros; third-order differential equation; distance between zeros},
language = {eng},
number = {1},
pages = {21-38},
title = {On distance between zeros of solutions of third order differential equations},
url = {http://eudml.org/doc/280745},
volume = {77},
year = {2001},
}

TY - JOUR
AU - N. Parhi
AU - S. Panigrahi
TI - On distance between zeros of solutions of third order differential equations
JO - Annales Polonici Mathematici
PY - 2001
VL - 77
IS - 1
SP - 21
EP - 38
AB - 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 $t_{n+1} - tₙ → ∞$ or $t_{n+2} - tₙ → ∞$ 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).
LA - eng
KW - zeros of solutions; lower bounds of zeros; third-order differential equation; distance between zeros
UR - http://eudml.org/doc/280745
ER -