Electron. J. Diff. Equ., Vol. 2010(2010), No. 51, pp. 1-5.

Oscillation criteria for semilinear elliptic equations with a damping term in R^n

Tadie

Abstract:
We use a method based on Picone-type identities to find oscillation conditions for the equation
$$ \sum_{i j =1}^n \frac{\partial}{\partial x_i} \Big( a_{ij}(x) \frac{\partial}{\partial x_j} \Big)u + f(x,u,\nabla u) + c(x) u \,, $$
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 9, 2010.
Math Subject Classifications: 35J60, 35J70.
Key Words: Picone's identity; semilinear elliptic equations.

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Tadie
Mathematics Institut, Universitetsparken 5
2100 Copenhagen, Denmark
email: tad@math.ku.dk

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