Differential equations of even-order with p-Laplacian like operators: qualitative properties of the solutions

Abstract In this paper, we study the oscillation of solutions for an even-order differential equation with middle term, driven by a p -Laplace operator form $$ \textstyle\begin{cases} ( r x ) \Phi _{p}[z^{ \kappa -1 } ] ^{\prime }+a _{p}[f z^{ ]+ \sum_{i=1}^{j}q_{i} _{p}[h z \delta _{i} ]=0, \\ \quad j\geq 1, >0, r^{\prime +a \geq 0, x\geq x_{0}>0. \end{cases}$$ { ( r x ) ? p [ z ? ? 1 ] ? + a f ? i = j q h ? 0 , ? > . The criteria these equations have been obtained. Furthermore, example is given to illustrate criteria.