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Integral averages and oscillation criteria for half-linear partial differential equation. (English) Zbl 1046.35034
The aim of this paper is to extend the technique of weighted integral averages to the half-linear partial differential equation $$\Delta_p u+ c(x)\Phi(u)= 0,\tag E$$ where $\Delta_p u\equiv \text{div}(\Vert u\Vert^{p-2}\nabla u)$, $p> 1$ is the $p$-Laplacian, $\Phi(u)=\vert u\vert^{p-2} u=\vert u\vert^{p-1}\text{sgn }u$, and $x= (x_i)^n_{i=1}\in \bbfR^n$. On the one hand, the author obtains new oscillation criteria for (E) which can remove the disadvantage of some previous theorems, and on the other hand he shows that this technique allows to obtain oscillation criteria not only for the exterior of a ball, but also for different types of unbounded domains. Some illustrative examples are given.

##### MSC:
 35J60 Nonlinear elliptic equations 35B05 Oscillation, zeros of solutions, mean value theorems, etc. (PDE)
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##### References:
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