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Zbl 1007.39018
Shen, J.H.; Stavroulakis, I.P.
Sharp conditions for nonoscillation of functional equations. (English)
[J] Indian J. Pure Appl. Math. 33, No.4, 543-554 (2002). ISSN 0019-5588; ISSN 0975-7465/e

The authors consider a couple of functional equations related to the realm of second-order linear difference equations with continuous arguments, for which previous work in the last ten years has concentrated mainly on necessary and sufficient conditions entailing the oscillatory nature of all solutions, and little attention has been given to the nonoscillatory ones. \par The paper is devoted to consider sharp conditions guaranteeing the existence of nonoscillatory solutions for these equations. In one of the two cases dealt with, the authors improve and generalize the incipient known results using arguments relying on a couple of ground results of functional analysis. For the other case the study is reduced to the detailed consideration of several first-order nonlinear functional equations.
[Claudi Alsina (Barcelona)]

MSC 2000:: *39B22 Functional equations for real functions
39A11 Stability of difference equations

Keywords: second-order linear difference equations; nonoscillatory solutions; first-order nonlinear functional equations

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