Opuscula Math. 37, no. 3 (), 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.