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On the complex oscillation of higher order linear differential equations

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In this paper, we investigate the growth of solutions and the existence of subnormal solutions for a class of higher order linear differential equations. We obtain some results which improve and extend the results of Chen-Shon [2] and Gundersen-Steinbart [5].

Abstract

In this paper, we investigate the growth of solutions and the existence of subnormal solutions for a class of higher order linear differential equations. We obtain some results which improve and extend the results of Chen-Shon [2] and Gundersen-Steinbart [5].

참고문헌 (10)

  1. T. B. Cao, "On the complex oscillation of higher order linear differential equations with meromorphic coefficients", J. Syst. Sci. Complex, 20(1), pp.135~148 (2007)
  2. Z. X. Chen, "On subnormal solutions of second order linear periodic differential equations", Sci. China Ser. A, 50(6), pp.786~800 (2007)
  3. Y. M. Chiang, "On a problem in complex oscillation theory of periodic second order linear differential equations and some related perturbation results", Ann. Acad. Sci. Fenn. Math., 27(2), pp.273~290 (2002)
  4. G. Gundersen, "Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates", J. London Math. Soc., 37(1), pp.88~104 (1988)
  5. G. Gundersen, "Subnormal solutions of second order linear differential equations with periodic coefficients", Results Math, 25(3), pp.270~289 (1994)
  6. G. Jank, "Einf¨uhrung in die Theorie der ganzen und Meromorphen Funktionen mit Anwendungen auf Differentialgleichungen" (1985), Birkh¨auser Verlag
  7. L. Kinnunen, "Linear differential equations with solutions of finite iterated order", Southeast Asian Bull. Math, 22(4), pp.385~405 (1998)
  8. I. Laine, "Nevanlinna Theory and Complex Differential Equations, de Gruyter Studies in Mathematics", pp.15~ (1993), Walter de Gruyter & Co
  9. H. Wittich, "Subnormale Losungen der Differentialgleichung: w00+p(ez)w0+q(ez)w = 0", Nagoya Math. J., 30, pp.29~37 (1967)
  10. C. C. Yang, "Uniqueness Theory of Meromorphic Functions, Mathematics and its Applications", pp.557~ (2003), Kluwer Academic Publishers Group

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