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

Abstract

We use a method based on Picone-type identities to find oscillation conditions for the equation $$ sum_{i j =1}^n frac{partial}{partial x_i} Big( a_{ij}(x) frac{partial}{partial x_j} Big)u + f(x,u, abla u) + c(x) u =0,, $$ 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.

Keywords

• Picone's identity
• semilinear elliptic equations