TY - JOUR

T1 - Sums of zeros of solutions to non-homogeneous ODE with polynomial coefficients

AU - Gil, Michael

N1 - Publisher Copyright:
© 2014 Elsevier Inc.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - We consider the equation u″=P(z)u+F(z) (z∈C), where P(z) is a polynomial and F(z) is an entire function. Let zk(u), k=1, 2, . . ., be the zeros of a solution u(z) to that equation. Estimates for the sums ∑k=1j1|zk(u)| (j=1, 2, . . .) are derived. In particular, they give us bounds for the zero free domain. Applications of the obtained estimates to the counting function of the zeros of solutions are also discussed.

AB - We consider the equation u″=P(z)u+F(z) (z∈C), where P(z) is a polynomial and F(z) is an entire function. Let zk(u), k=1, 2, . . ., be the zeros of a solution u(z) to that equation. Estimates for the sums ∑k=1j1|zk(u)| (j=1, 2, . . .) are derived. In particular, they give us bounds for the zero free domain. Applications of the obtained estimates to the counting function of the zeros of solutions are also discussed.

KW - ODE in the complex plane

KW - Zeros of solutions

UR - http://www.scopus.com/inward/record.url?scp=84922650679&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2014.06.045

DO - 10.1016/j.jmaa.2014.06.045

M3 - Article

AN - SCOPUS:84922650679

VL - 421

SP - 1917

EP - 1924

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -