Bounds for Products of Zeros of Solutions to Nonhomogeneous ODE with Polynomial Coefficients

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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. Lower estimates for the products Πk=1j | zk(u) | (j = 1,2,⋯) are derived. In particular, they give us a bound for the zero free domain. Applications of the obtained estimates to the counting function of the zeros of solutions are also discussed.

Original languageEnglish
Article number690519
JournalInternational Journal of Differential Equations
Volume2015
DOIs
StatePublished - 1 Jan 2015

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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