## Riccati-type inequality and oscillation criteria for a half-linear PDE with damping.(English)Zbl 1043.35018

This paper deals with the study of the partial Riccati-type differential inequality $\text{div\,}\vec w+ \|\vec w\|^q+ c(x)\leq 0$ and some generalizations of this inequality in the forms $\text{div}(\alpha(x)\vec w)+ K\alpha(x)\|\vec w\|^q+ \alpha(x) c(x)\leq 0$ and $\text{div\,}\vec w+ K\|\vec w\|^q+ c(x)+ \langle\vec w,\vec b\rangle\leq 0,$ where $$K\in \mathbb{R}$$, $$q> 1$$, and $$\alpha$$, $$c$$, $$b$$ are the given functions.
The author applies the obtained results to the oscillation of damped half-linear PDEs. Moreover, he presents some examples and comments. Unbounded domains and a special oscillation criterion for conic domains are also discussed.

### MSC:

 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35J60 Nonlinear elliptic equations
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