Mařík, Robert Riccati-type inequality and oscillation criteria for a half-linear PDE with damping. (English) Zbl 1043.35018 Electron. J. Differ. Equ. 2004, Paper No. 11, 17 p. (2004). 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. Reviewer: Messoud A. Efendiev (Berlin) Cited in 11 Documents MSC: 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35J60 Nonlinear elliptic equations Keywords:\(p\)-Laplacian; oscillatory solution; Riccati equation; half-linear equation; damped equation PDFBibTeX XMLCite \textit{R. Mařík}, Electron. J. Differ. Equ. 2004, Paper No. 11, 17 p. (2004; Zbl 1043.35018) Full Text: EMIS