Opuscula Math. 37, no. 3 (2017), 389-402

Opuscula Mathematica

General solutions of second-order linear difference equations of Euler type

Akane Hongyo
Naoto Yamaoka

Abstract. The purpose of this paper is to give general solutions of linear difference equations which are related to the Euler-Cauchy differential equation \(y^{\prime\prime}+(\lambda/t^2)y=0\) or more general linear differential equations. We also show that the asymptotic behavior of solutions of the linear difference equations are similar to solutions of the linear differential equations.

Keywords: Euler-Cauchy equations, oscillation, conditionally oscillatory.

Mathematics Subject Classification: 39A06, 39A12, 39A21.

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  • Akane Hongyo
  • Osaka Prefecture University, Department of Mathematical Sciences, Sakai 599-8531, Japan
  • Naoto Yamaoka
  • Osaka Prefecture University, Department of Mathematical Sciences, Sakai 599-8531, Japan
  • Communicated by P.A. Cojuhari.
  • Received: 2016-08-30.
  • Revised: 2016-09-30.
  • Accepted: 2016-09-30.
  • Published online: 2017-01-30.
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Cite this article as:
Akane Hongyo, Naoto Yamaoka, General solutions of second-order linear difference equations of Euler type, Opuscula Math. 37, no. 3 (2017), 389-402, http://dx.doi.org/10.7494/OpMath.2017.37.3.389

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