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2009•Journal of South China Normal UniversityRequires access

THE COMPLEX OSCILLATION OF A CLASS OF HIGHER ORDER DIFFERENTIAL EQUATION

Zong-Xuan Chen

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Abstract

The growth of solutions of the differential equation f(k)+Hk-1(z)f(k-1)+…+H0(z)f=F(z)is investigated,where Hj(z)=Aj(z)ePj(z)(j=0,1,…,k-1),Aj(z),F(z)are entire functions,σ(Aj)n,pj(z)(j=0,1,…,k-1)are polynomials.The results in the existing references are improved and a precise estimate of the growth rate of solutions is obtained for the equations when H0(z)is dominating to the properties of solutions of the equation.

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What this paper is about

The growth of solutions of the differential equation f(k)+Hk-1(z)f(k-1)+…+H0(z)f=F(z)is investigated,where Hj(z)=Aj(z)ePj(z)(j=0,1,…,k-1),Aj(z),F(z)are entire functions,σ(Aj)n,pj(z)(j=0,1,…,k-1)are polynomials.The results in the existing references are improved and a precise estimate of the growth rate of solutions is obtained for the equations when H0(z)is dominating to the properties of solutions of the equation.

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Available abstract

The growth of solutions of the differential equation f(k)+Hk-1(z)f(k-1)+…+H0(z)f=F(z)is investigated,where Hj(z)=Aj(z)ePj(z)(j=0,1,…,k-1),Aj(z),F(z)are entire functions,σ(Aj)n,pj(z)(j=0,1,…,k-1)are polynomials.The results in the existing references are improved and a precise estimate of the growth rate of solutions is obtained for the equations when H0(z)is dominating to the properties of solutions of the equation.

Key concepts: Oscillation (cell signaling), Differential equation, Mathematics, Order (exchange), Class (philosophy), Entire function, Mathematical analysis, Physics

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