Articles

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

  • Michael Gil’
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  • Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel

Received date: 2010-10-07

  Online published: 2012-05-20

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)|.

Cite this article

Michael Gil’ . PERTURBATIONS OF ZEROS OF SOLUTIONS TO SECOND ORDER DIFFERENTIAL EQUATIONS WITH POLYNOMIAL COEFFICIENTS[J]. Acta mathematica scientia, Series B, 2012 , 32(3) : 1083 -1092 . DOI: 10.1016/S0252-9602(12)60081-2

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