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 -