Oscillation Theorems for Quasilinear Elliptic Differential Equations

By using vector Riccati transformation and averaging technique, some oscillation criteria for the quasilinear elliptic di.erential equation of second order, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sum\limits_{i,j = 1}^N {D_i \left[ {\Psi \left( y \right)A_{ij} \left( x \right)\left| {Dy} \right|^{p - 2} D_j y} \right] + p\left( x \right)f\left( y \right)} = 0, $$\end{document}are obtained. These theorems extend and include earlier results for the semilinear elliptic equation and PDE with p-Laplacian.