Averaging technique and nonlinear second order elliptic oscillation

By using the refinement of the standard integral averaging technique, we obtain new oscillation criteria for certain nonlinear second order damped elliptic differential equations. We do not impose any additional conditions on the damping terms except for the continuity. In particular, when N=1N=1, our results extend those of Rogovchenko and Tuncay [Yu.V. Rogovchenko, F. Tuncay, Oscillation criteria for second-order nonlinear differential equations with damping, Nonlinear Analysis 69 (2008) 208–221] for second-order nonlinear differential equations with damping to damped elliptic differential equations. When N≥2N≥2, our results improve the oscillation criteria of Xu, Jia, Ma [Z. Xu, B. Jia, D. Ma, Oscillation theorems for elliptic equations with damping, Appl. Math. Comput, 156 (2004) 93–106] for second order elliptic equations with damping. Four examples are provided to illustrate the relevance of the main results.