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For a second order linear differential equation $f''+A(z)f'+B(z)f=0$, with $ A(z)$ and $B(z)$ being transcendental entire functions under some restrictions, we have established that all non-trivial solutions are of infinite order. In addition, we have proved that these solutions, with a condition, have exponent of convergence of zeros equal to infinity. Also, we have extended these results to higher order linear differential equations.
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참고문헌 (23)
참고문헌 신청
I. Amemiya / 1981 / Nonexistence of finite order solutions of w" + e-zw' +Q(z)w = 0 / Hokkaido Math. J. 10(Special Issue):1~17
S. B. Bank / 1986 / On the frequency of zeros of solutions of second order linear differential equations / Results Math. 10(1-2):8~24
P. D. Barry / 1963 / On a theorem of Besicovitch / Quart. J. Math. Oxford Ser. (2) 14(2):293~302
A. S. Besicovitch / 1927 / On integral functions of order < 1 / Math. Ann. 97(1):677~695
M. Frei / 1962 / Uber die subnormalen Losungen der Differentialgleichung w"+e-z ·w'+konst.·w = 0 / Comment. Math. Helv 36:1~8
S. B. Bank / 1986 / On the frequency of zeros of solutions of second order linear differential equations / Results Math. 10(1-2):8~24
P. D. Barry / 1963 / On a theorem of Besicovitch / Quart. J. Math. Oxford Ser. (2) 14(2):293~302
A. S. Besicovitch / 1927 / On integral functions of order < 1 / Math. Ann. 97(1):677~695
M. Frei / 1962 / Uber die subnormalen Losungen der Differentialgleichung w"+e-z ·w'+konst.·w = 0 / Comment. Math. Helv 36:1~8
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