Ramayyan, A.; Thandapani, E. Second order linear difference equations over discrete Hardy fields. (English) Zbl 1274.39012 Kybernetika 34, No. 2, 181-187 (1998). Summary: We shall investigate the properties of solutions of second order linear difference equations defined over a discrete Hardy field via canonical valuations. MSC: 39A10 Additive difference equations Keywords:discrete Hardy field; second order difference equation PDFBibTeX XMLCite \textit{A. Ramayyan} and \textit{E. Thandapani}, Kybernetika 34, No. 2, 181--187 (1998; Zbl 1274.39012) Full Text: Link References: [1] Agarwal R. P.: Difference Equations and Inequalities. Marcel Dekker, New York 1992 · Zbl 0952.39001 [2] Boshernitzan M.: New orders of infinity. J. Analyse Math. 41 (1982), 130-167 · Zbl 0539.26003 · doi:10.1007/BF02803397 [3] Boshernitzan M.: Discrete orders of infinity. Amer. J. Math. 106 (1984), 1147-1198 · Zbl 0602.26003 · doi:10.2307/2374277 [4] Mickens R. R.: Difference Equations. Van Nostrand Reinhold, New York 1990 · Zbl 0963.39005 · doi:10.1080/10236190008808233 [5] Ramayyan A.: On \(n\)th order differential equations over Hardy fields. Kybernetika 30 (1994), 461-470 · Zbl 0822.34033 [6] Rosenlicht M.: Hardy fields. J. Math. Anal. Appl. 93 (1983), 294-311 · Zbl 0518.12014 · doi:10.1016/0022-247X(83)90175-0 [7] Rosenlicht M.: The rank of a Hardy field. Trans. Amer. Math. Soc. 280 (1983), 659-671 · Zbl 0536.12015 · doi:10.2307/1999639 [8] Rosenlicht M.: Asymptotic solution of \(y^{\prime \prime }=F(x)\,y\). J. Math. Anal. Appl. 189 (1995), 640-650 · Zbl 0824.34068 · doi:10.1006/jmaa.1995.1042 [9] Thandapani E., Graef J. R., Spikes P. W.: Monotonicity and summability of solution of a second order nonlinear difference equation. Bull. Inst. Math. Acad. Sinica 23 (1995), 343-356 · Zbl 0845.39003 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.