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.