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Zbl 1043.35018
Mař\'ik, Robert
Riccati-type inequality and oscillation criteria for a half-linear PDE with damping. (English)
[J] Electron. J. Differ. Equ. 2004, Paper No. 11, 17 p., electronic only (2004). ISSN 1072-6691/e

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.\par 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.
[Messoud A. Efendiev (Berlin)]

MSC 2000:: *35B05 General behavior of solutions of PDE
35J60 Nonlinear elliptic equations

Keywords: $p$-Laplacian; oscillatory solution; Riccati equation; half-linear equation; damped equation

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