Oscillation of second order semilinear elliptic equations with damping

Abstract

We obtain some new Kamenev-type oscillation theorems for the second order semilinear elliptic differential equation with damping $$ \sum\limits_{i,j = 1}^N {D\left[ {a_{ij} \left( x \right)D_j y} \right] + } \sum\limits_{i = 1}^N {b_i \left( x \right)D_i y + c\left( x \right)f\left( y \right) = 0} $$ under quite general assumptions. These results are extensions of the recent results of Sun [Sun, Y. G.: New Kamenev-type oscillation criteria of second order nonlinear differential equations with damping. J. Math. Anal. Appl., 291, 341–351 (2004)] in a natural way. In particular, we do not impose any additional conditions on the damped functions bi(x) except the continuity. Several examples are given to illustrate the main results.