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In this paper we discuss the classical problem of finding conditions on the entire coefficients $A(z)$ and $B(z)$ guaranteeing that all nontrivial solutions of $f''+A(z)f'+B(z)f=0$ are of infinite order. We assume $A(z)$ is an entire function of completely regular growth and $B(z)$ satisfies three different conditions, then we obtain three results respectively. The three conditions are (1) $B(z)$ has a dynamical property with a multiply connected Fatou component, (2) $B(z)$ satisfies $T(r,B)\sim \log M(r,B)$ outside a set of finite logarithmic measure, (3) $B(z)$ is extremal for Denjoy's conjecture.
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참고문헌 (38)
참고문헌 신청
L. Ahlfors / 1930 / Untersuchungen zur Theorie der konformen abbildung und der Theorie der ganzen Funktionen / Acta Soc. Sci. Fenn 1:1~40
Irvine Noel Baker / 1963 / Multiply connected domains of normality in iteration theory / Mathematische Zeitschrift 81(3):206~214
I. N. Baker / 1975 / The domains of normality of an entire function / Ann. Acad. Sci. Fenn. Ser. A I Math 1(2):277~283
I. N. Baker / 1976 / An entire function which has wandering domains / Journal of the Australian Mathematical Society 22(2):173~176
Walter Bergweiler / 1993 / Iteration of meromorphic functions / Bulletin of the American Mathematical Society 29(2):151~188
Irvine Noel Baker / 1963 / Multiply connected domains of normality in iteration theory / Mathematische Zeitschrift 81(3):206~214
I. N. Baker / 1975 / The domains of normality of an entire function / Ann. Acad. Sci. Fenn. Ser. A I Math 1(2):277~283
I. N. Baker / 1976 / An entire function which has wandering domains / Journal of the Australian Mathematical Society 22(2):173~176
Walter Bergweiler / 1993 / Iteration of meromorphic functions / Bulletin of the American Mathematical Society 29(2):151~188
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