Oscillation criteria of Kamenev-type for non-linear partial differential equations

Abstract

Using the technique of weighted integral averages, known in the oscillation theory of ordinary differential equations, we obtain new oscillation criteria for the non-linear partial differential equation 1\\quad{\\rm and}\\ u\\geq u_{0}, \\end{align*}$$]]> div ( ‖ ∇ y ‖ p − 2 ∇ y ( 1 + ‖ ∇ y ‖ p ) p − 1 p ) + f ( u ) | y | p − 2 y ( 1 − | y | p ) p − 1 p = 0 , p > 1 and u ≥ u 0 , on unbounded domains.