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Existence of radial solutions for an elliptic problem involving exponential nonlinearities
| 1. | Dip. di Matematica, Università di Roma "La Sapienza", P.le A.Moro 2 - 00185 - Roma |
$-\Delta u+a(|x|)u=\lambda e^u$in$\ B_1,$ (0.1)
$u=0$ on$ \partial B_1.$
where $B_1$ is the unit ball in $R^N$, $N\ge2$, $\lambda>0$ and $a(|x|)\ge0$ is a smooth radial function.
Under some suitable assumptions on the regular part of the Green function of the operator
$-u''- \frac{N-1}{r}u+a(r)u$, we prove the existence of a radial solution to (0.1)
for $\lambda$ small enough.
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