The Hyperorder of Solutions of Second-Order Linear Differential Equations

Abstract

We prove that the hyperorder of every nontrivial solution of homogenous linear differential equations of type $f\mathrm{\prime }\mathrm{\prime }+A_{\mathrm{1}}(z)e^{az}f\mathrm{\prime }+A_{\mathrm{0}}(z)e^{bz}f=\mathrm{0}$ and nonhomogeneous equation of type $f\mathrm{\prime }\mathrm{\prime }+A_{\mathrm{1}}(z)e^{az}f\mathrm{\prime }+A_{\mathrm{0}}(z)e^{bz}f=H(z)$ is one, where $A_{\mathrm{0}},A_{\mathrm{1}},H(z)$ are entire functions of order less than one, improving the previous results of Chen, Wang, and Laine.