Kodai Mathematical Journal | |
On the frequency of complex zeros of solutions of certain differential equations | |
Steven B. Bank1  | |
[1] DEPARTMENT OF MATHEMATICS UNIVERSITY OF ILLINOIS | |
关键词: Multivalued operator; monotone operator; measurable multifunction; upper and lower semicontinuous multifunctions; evolution triple; compact embedding; Shauder-Tichonov fixed point theorem; periodic trajectories; | |
DOI : 10.2996/kmj/1138039595 | |
学科分类:数学(综合) | |
来源: Tokyo Institute of Technology, Department of Mathematics | |
【 摘 要 】
References(20)In this paper, we investigate the frequency of zeros of solutions of linear differential equations of the form w(k)+∑\limits{\jmath}=1k−1Qjw(j)+(Q0+ReP)w=0, where k{≥}2, and where Q0, …, Qk−1, R and P are arbitrary polynomials with R{¬≡}0 and P non-constant. All solutions f{¬≡}0 of such an equation are entire functions of infinite order of growth, but there are examples of such equations which can possess a solution whose zero-sequence has a finite exponent of convergence. In this paper, we show that unless a special relation exists between the polynomials Q0, …, Qk−1, and P, all solutions of such an equation have an infinite exponent of convergence for their zero-sequences. This result extends earlier results for the equation, w(k)+(Q0+ReP)w=0.
【 授权许可】
Unknown
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