Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 51, pp. 1-5.

Title: Oscillation criteria for semilinear elliptic equations with
      a damping term in R^n
       
Author: Tadie (Universitetsparken 5, Copenhagen, Denmark)

Abstract:
 We use a method based on Picone-type identities to find
 oscillation conditions for the equation
 $$
 \sum_{i j =1}^n \frac{\partial}{\partial x_i}
 \Big( a_{ij}(x) \frac{\partial}{\partial x_j} \Big)u +
 f(x,u,\nabla u)  + c(x) u =0\,,
 $$
 with Dirichlet boundary conditions on bounded and unbounded domains.
 In this article, the above method substitudes the traditional Riccati 
 techniques [3,8] used for unbounded domains.

Submitted September 10, 2009. Published April 09, 2010.
Math Subject Classifications: 35J60, 35J70.
Key Words: Picone's identity; semilinear elliptic equations.