Philos-type oscillation theorems for second order damped elliptic equations

Abstract

Using general means, we establish several new Philos-type oscillation theorems for the second order damped elliptic differential equation $$ \sum\limits_{i,j = 1}^N {D_i \left[ {a_{ij} (x)D_j y} \right]} + \sum\limits_{i = 1}^N {b_i (x)D_i y + c(x)f(y) = 0} $$ under quite general assumptions. The obtained results are extensions of the well-known oscillation results due to Kamenev, Philos, Yan for second order linear ordinary differential equations and improve recent results of Xu, Jia and Ma.