ON A PROBLEM IN COMPLEX OSCILLATION THEORY OF PERIODIC HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

doi:10.1016/S0252-9602(10)60125-7

Abstract

Abstract:

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(e^z), B(ς)=g₁(1/ς)+g₂(ς), g₁and 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, …, f_k of Eq.(*) satisfy λ_e(f₁… f_k) ≥ο(g₂) under the condition that f_j(z) and f_j(z+2πi )(j =1, …, k) are linearly dependent.

Key words: Differential equation, periodic, linearly dependent, complex oscillation

CLC Number:

30D35

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.

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ON A PROBLEM IN COMPLEX OSCILLATION THEORY OF PERIODIC HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

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