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

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Abstract

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 ̃)|.

Original languageEnglish
Pages (from-to)1083-1092
Number of pages10
JournalActa Mathematica Scientia
Volume32
Issue number3
DOIs
StatePublished - 1 May 2012

Keywords

  • 34A30
  • 34C10
  • Complex differential equation
  • Perturbation of zeros
  • Zeros of solutions

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