Behavior of positive radial solutions for quasilinear elliptic equations

García-Huidobro, Marta; Manásevich, Raúl; Yarur, Cecilia

doi:10.1090/S0002-9939-00-05951-7

Behavior of positive radial solutions for quasilinear elliptic equations
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by Marta García-Huidobro, Raúl Manásevich and Cecilia S. Yarur PDF

Proc. Amer. Math. Soc. 129 (2001), 381-388 Request permission

Abstract:

We establish a necessary and sufficient condition so that positive radial solutions to \begin{equation*} -\textrm {div} (A(|\nabla u|)\nabla u) = f(u),\quad \mbox {in}~~ B_{R}(0)\setminus \{0\},\ R>0, \end{equation*} having an isolated singularity at $x=0$, behave like a corresponding fundamental solution. Here, $A:\mathbb R\setminus \{0\}\to \mathbb R$ and $f:[0,\infty )\to [0,\infty )$ are continuous functions satisfying some mild growth restrictions.

References

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