OSCILLATION AND NONOSCILLATION OF SOLUTIONS OF PDE WITH $p$−LAPLACIAN

Abstract

Some necessary conditions are established for the nonoscillation of the following PDE with $p-$Laplacian \begin{equation*} \mbox{div}(\|\nabla y\|^{p-2}\nabla y)+c(x)|y|^{p-2}y=0. \end{equation*} Using these results, we obtain some oscillation criteria for the above equation.