TY - JOUR

T1 - Perturbation of zeros of solutions to second order differential equations with polynomial coefficients

AU - Gil', Michael

PY - 2012/5/1

Y1 - 2012/5/1

N2 - Let P(z) and P ̃(z) be polynomials of the same degree. We consider the equations . u' = . P(. z). u and u ̃''=P ̃(z)u ̃ (z∈) whose solutions are u(z) and u ̃(z), respectively. Let . z k(u) and zk(u tild;),k=1,2,..., be the zeros of u(z) and u ̃(z), respectively. We derive bounds for the quantity. kinf|1zk(u)-1zj(u ̃)|.

AB - Let P(z) and P ̃(z) be polynomials of the same degree. We consider the equations . u' = . P(. z). u and u ̃''=P ̃(z)u ̃ (z∈) whose solutions are u(z) and u ̃(z), respectively. Let . z k(u) and zk(u tild;),k=1,2,..., be the zeros of u(z) and u ̃(z), respectively. We derive bounds for the quantity. kinf|1zk(u)-1zj(u ̃)|.

KW - 34A30

KW - 34C10

KW - Complex differential equation

KW - Perturbation of zeros

KW - Zeros of solutions

UR - http://www.scopus.com/inward/record.url?scp=84861317134&partnerID=8YFLogxK

U2 - 10.1016/S0252-9602(12)60081-2

DO - 10.1016/S0252-9602(12)60081-2

M3 - Article

AN - SCOPUS:84861317134

VL - 32

SP - 1083

EP - 1092

JO - Acta Mathematica Scientia

JF - Acta Mathematica Scientia

SN - 0252-9602

IS - 3

ER -