Opuscula Math. 37, no. 3 (2017), 389-402
http://dx.doi.org/10.7494/OpMath.2017.37.3.389
Opuscula Mathematica
General solutions of second-order linear difference equations of Euler type
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.
