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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2017, Vol. 32 Issue (4): 431-436    DOI:
    
Complex oscillation of solutions of some second order non-homogeneous linear di?erential equations#br#
YUAN Rong, LIU Hui-fang
College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China
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Abstract  In this paper, the growth and the distribution of zeros of solutions to some second order non-homogeneous differential equations $f''+A\text{e}^{az^n}f'+(B_1\text{e}^{bz^n}+B_0\text{e}^{dz^n})f=F(z)$ are investigated, where $F$ is a nonzero entire function with order less than $n$, $A, B_1, B_0$ are nonzero polynomials. Under an appropriate assumption on complex numbers $a, b, d$, the precise estimations on the hyper order and the hyper convergence exponent of zeros of solutions of such equation are obtained.

Key words： differential equation      entire function      hyper order      zero     
Received: 03 March 2017      Published: 01 December 2018
CLC:  O175.14  
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Cite this article:

YUAN Rong, LIU Hui-fang. Complex oscillation of solutions of some second order non-homogeneous linear di?erential equations#br#. Applied Mathematics A Journal of Chinese Universities, 2017, 32(4): 431-436.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2017/V32/I4/431


一类二阶非齐次线性微分方程解的复振荡

研究了一类二阶非齐次线性微分方程$f''+A\mathrm{e}^{az^n}f'+(B_1\mathrm{e}^{bz^n}+B_0\mathrm{e}^{dz^n})f=F(z)$ 解的增长性和零点分布, 其中$F$为级小于$n$的非零整函数,  $A, B_1, B_0$ 为非零多项 式. 在复数$a, b, d$满足一定条件下, 得到该方程的每一个解的超级和二级零点收敛指数的精确估计.

关键词： 微分方程,  整函数,  超级,  零点 
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