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On zeros and growth of solutions of second order linear differential equations

Sanjay Kumar|Manisha Saini
대한수학회 (The Korean Mathematical Society)|2020.01|대한수학회논문집 (Communications of the KMS)|제35권 제1호|pp. 229-241|DOI 10.4134/CKMS.c180494

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참고문헌

키워드

meromorphic functionEntire functionorder of growthexponent of convergencecomplex differential equation
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초록

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.

Abstract

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.

참고문헌 (23)

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