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Zbl 1046.35034
Mařík, Robert
Integral averages and oscillation criteria for half-linear partial differential equation. (English)
[J] Appl. Math. Comput. 150, No. 1, 69-87 (2004). ISSN 0096-3003

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 $x= (x_i)^n_{i=1}\in \bbfR^n$.\par 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.
[Marian Ivanovici (Craiova)]

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

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

Cited in: Zbl 1150.35040

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