数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (3): 1083-1092.doi: 10.1016/S0252-9602(12)60081-2

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PERTURBATIONS OF ZEROS OF SOLUTIONS TO SECOND ORDER DIFFERENTIAL EQUATIONS WITH POLYNOMIAL COEFFICIENTS

Michael Gil’   

  1. Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel
  • 收稿日期:2010-10-07 出版日期:2012-05-20 发布日期:2012-05-20

PERTURBATIONS OF ZEROS OF SOLUTIONS TO SECOND ORDER DIFFERENTIAL EQUATIONS WITH POLYNOMIAL COEFFICIENTS

Michael Gil’   

  1. Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel
  • Received:2010-10-07 Online:2012-05-20 Published:2012-05-20

摘要:

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∈C) whose solutions are u(z) and u(z), respectively. Let zk(u) and zk(u), k = 1, 2, … , be the zeros of u(z) and u(z), respectively. We derive bounds for the quantity

supjinfk |1/zk(u)-1/zk(u)|.
.

关键词: Complex differential equation, zeros of solutions, perturbation of zeros

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∈C) whose solutions are u(z) and u(z), respectively. Let zk(u) and zk(u), k = 1, 2, … , be the zeros of u(z) and u(z), respectively. We derive bounds for the quantity

supjinfk |1/zk(u)-1/zk(u)|.

Key words: Complex differential equation, zeros of solutions, perturbation of zeros

中图分类号: 

  • 34C10