Estimate of the Hyper-Order of Solutions for Certain Higher Order Linear Differential Equations

By utilizing Nevanlinna's value distribution theory of meromorphic functions and categorized discussion method, the growth of solutions of higher order differential equations is investigated and some important results are obtained.When Hj(z) (j=0,1,,k-1) are entire functions, according to the general theory of linear differential equations, every solution of the above equations with entire coefficients is entire function. When the coefficients of the above equations satisfy: Hj(z)=hj(z)ePj(z)(j=0,1,,k-1),Pj(z) are 〖JP2〗polynomials with degree n and leading coefficients aj, hj(z) are entire functions, (hj(z))s, as=dsei,〖JP〗 al=-dlei, ds0, dl0. For js,l, aj=djei(dj0) or aj=-djei, maxdj;js,l=d