Oscillation of Linear Ordinary Differential Equations: on a Theorem by A. Grigoriev

  title={Oscillation of Linear Ordinary Differential Equations: on a Theorem by A. Grigoriev},
  author={Sergei A Yakovenko},
We give a simplified proof and an improvement of a recent theorem by A. Grigoriev, placing an upper bound for the number of roots of linear combinations of solutions to systems of linear equations with polynomial or rational coefficients. 1. Background on counting zeros of solutions of linear ordinary differential equations 1.1. De la Valée Poussin theorem and Novikov’s counterexample. A linear nth order homogeneous differential equation y + a1(t) y (n−1) + · · · + an−1(t) y + an(t) y = 0, y… CONTINUE READING
2 Citations
10 References
Similar Papers


Publications referenced by this paper.
Showing 1-10 of 10 references

Singular perturbations and zeros of Abelian integrals

  • A. Grigoriev
  • Weizmann Institute of Science (Rehovot),
  • 2001

On the number of zeros of analytic functions in a neighborhood of a Fuchsian singular point with real spectrum

  • M. Roitman, S. Yakovenko
  • Math. Res. Lett
  • 1996

Distribution of zeros of entire functions, revised ed

  • B. Ja. Levin
  • Translations of Mathematical Monographs,
  • 1980

Singular points of complex hypersurfaces

  • J. Milnor
  • Annals of Mathematics Studies,
  • 1968

Similar Papers

Loading similar papers…