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.


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