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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 $$\text{div }\vec w+ \Vert\vec w\Vert^q+ c(x)\le 0$$ and some generalizations of this inequality in the forms $$\text{div}(\alpha(x)\vec w)+ K\alpha(x)\Vert\vec w\Vert^q+ \alpha(x) c(x)\le 0$$ and $$\text{div }\vec w+ K\Vert\vec w\Vert^q+ c(x)+ \langle\vec w,\vec b\rangle\le 0,$$ where $K\in \bbfR$, $q> 1$, 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.

35B05Oscillation, zeros of solutions, mean value theorems, etc. (PDE)
35J60Nonlinear elliptic equations
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