In this paper the authors classified all solutions of the second-order nonlinear neutral differential equations of mixed type,into four classes and obtained conditions for the existence/non-existence of solutions in these classes. Examples are provided to illustrate the main results. MSC: 34C15
Self-consistent ab initio calculations are performed on the structural, electronic and optical properties of wurtzite ZnO. The Full Potential Linearized Augmented Plane Wave (FP-LAPW) method is applied to solve the Kohn-Sham equations. Results are obtained by using the PBE-GGA and mBJLDA exchange correlation potentials. The energy and charge convergence have been examined to study the ground state properties. The band structure and Density of States (DOS) diagrams are plotted from the calculated equilibrium lattice parameters. The general profiles of the optical spectra and the optical properties, including the real and imaginary part of dielectric function, reflectivity, refractive index, absorption coefficient , electron energy loss function and optical conductivity of wurtzite ZnO under ambient conditions are discussed. The optical anisotropy is studied through the calculated optical constants, namely dielectric function and refractive index along three different crystallographic axes.
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