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

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)1917-1924
Number of pages8
JournalJournal of Mathematical Analysis and Applications
Volume421
Issue number2
DOIs
StatePublished - 1 Jan 2015

Keywords

  • ODE in the complex plane
  • Zeros of solutions

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Sums of zeros of solutions to non-homogeneous ODE with polynomial coefficients'. Together they form a unique fingerprint.

Cite this