The radial oscillation of solutions to ode's in the complex domain
The radial oscillation of solutions to ode's in the complex domain
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DOI：
10.1017/s0013091500023233
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发表时间：
1996-10
影响因子：
0.7
通讯作者：
J. Rossi;Shupei Wang
中科院分区：
文献类型：
--
作者：
J. Rossi;Shupei Wang
证明了（*）w″ + Aw = 0解在射线附近的振动性的三个结果，其中A是整函数.第一个结果假设A是多项式，并给出了它的真实的零点个数的上界，如果（*）允许一个解只有真实的零点且无穷多个。第二个结果证明了对于有限阶的A，解w在射线附近有“几个”零点当且仅当对w′也是如此。第三个结果涉及（*）“远离”有限射线集的解的零点的密度。
We prove three results concerning the oscillation near a ray of solutions to (*)w″ + Aw = 0, where A is an entire function. The first result assumes that A is a polynomial and gives an upper bound on the number of its real zeros if (*) admits a solution with only real zeros and infinitely many. The second result proves that for A of finite order a solution w to (*) has “few” zeros “near” a ray if and only if the same is true for w′. The third result involves the density of the zeros of a solution to (*) “away” from a finite set of rays.