Acta mathematica scientia, Series B >
ON A PROBLEM IN COMPLEX OSCILLATION THEORY OF PERIODIC HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS
Received date: 2007-12-30
Revised date: 2008-10-20
Online published: 2010-07-20
Supported by
This work is supported by the National Natural Foundation of China (10871076) and the Startup Foundation for Doctors of Jiangxi Normal University (2614)
In this article, the zeros of solutions of differential equation
f(k)}(z)+A(z)f(z)=0, (*)
are studied, where k>2, A(z)=B(ez), B(ς)=g1(1/ς)+g2(ς), g1 and g2 being entire functions with g2 transcendental and ο(g2) not equal to a positive integer or infinity. It is shown that any linearly independent solutions f1, f2, …, fk of Eq.(*) satisfy λe(f1… fk) ≥ο(g2) under the condition that fj(z) and fj(z+2πi )(j =1, …, k) are linearly dependent.
Key words： Differential equation; periodic; linearly dependent; complex oscillation
XIAO Li-Peng , CHEN Zong-Xuan . ON A PROBLEM IN COMPLEX OSCILLATION THEORY OF PERIODIC HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS[J]. Acta mathematica scientia, Series B, 2010 , 30(4) : 1291 -1300 . DOI: 10.1016/S0252-9602(10)60125-7
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