# IJPAM: Volume 67, No. 1 (2011)

QUASILINEAR ELLIPTIC EQUATIONS WITH A DAMPING
TERM VIA PICONE-TYPE IDENTITIES:
OSCILLATORY SOLUTIONS AND UNIQUENESS

Institute of Mathematics
5, Universitetsparken
Copenhagen, 2100, DENMARK

Abstract.We establish a uniqueness theorem and some oscillation criterion for the equation

We use solely some selected Picone's type formulas and the known such results for the related half linear equation. The work is an extension of the earlier one on semilinear equations (see [#!t3!#]). This work underlines the fact that such results can follow mainly from some properties of the main coefficients and of the equation. The usual methods based on the Riccati techniques (see [#!m1!#], [#!xu!#]) make our methods quite simple. Equations with Laplacian displayed above and associated half-linear equations (when ) have been widely investigated lately because of the interest in their applications (e.g. in physical and biological problems, see, e.g. [#!d2!#], [#!m1!#] and referrences therein).