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Article

Keywords:
discrete Hardy field; second order difference equation
Summary:
We shall investigate the properties of solutions of second order linear difference equations defined over a discrete Hardy field via canonical valuations.
References:
[1] Agarwal R. P.: Difference Equations and Inequalities. Marcel Dekker, New York 1992 MR 1155840 | Zbl 0952.39001
[2] Boshernitzan M.: New orders of infinity. J. Analyse Math. 41 (1982), 130–167 DOI 10.1007/BF02803397 | MR 0687948 | Zbl 0539.26003
[3] Boshernitzan M.: Discrete orders of infinity. Amer. J. Math. 106 (1984), 1147–1198 DOI 10.2307/2374277 | MR 0761583 | Zbl 0602.26003
[4] Mickens R. R.: Difference Equations. Van Nostrand Reinhold, New York 1990 MR 1158461 | Zbl 0963.39005
[5] Ramayyan A.: On $n$th order differential equations over Hardy fields. Kybernetika 30 (1994), 461–470 MR 1303296 | Zbl 0822.34033
[6] Rosenlicht M.: Hardy fields. J. Math. Anal. Appl. 93 (1983), 294–311 MR 0700146 | Zbl 0518.12014
[7] Rosenlicht M.: The rank of a Hardy field. Trans. Amer. Math. Soc. 280 (1983), 659–671 DOI 10.1090/S0002-9947-1983-0716843-5 | MR 0716843 | Zbl 0536.12015
[8] Rosenlicht M.: Asymptotic solution of $y^{\prime \prime }=F(x)\,y$. J. Math. Anal. Appl. 189 (1995), 640–650 DOI 10.1006/jmaa.1995.1042 | MR 1312544
[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 MR 1367370
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