Asymptotic estimates for PDE with p-Laplacian and damping

R. Marik, Mendel University, Brno, Czech Republic

E. J. Qualitative Theory of Diff. Equ., No. 5. (2005), pp. 1-6.

Abstract: We study the positive solutions of equation
\begin{equation*}
\div(\norm{\nabla u}^{p-2}\nabla u)+\ss{\vec b(x)}{\norm{\nabla
u}^{p-2}\nabla u}+c(x)|u|^{q-2}u=0,
\end{equation*}
via the Riccati technique and prove an integral sufficient condition on the potential function $c(x)$ and the damping $\vec b(x)$ which ensures that no positive solution of the equation satisfies a lower (if $p>q$) or upper (if $q>p$) bound eventually.

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