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January  2008, 21(1): 221-232. doi: 10.3934/dcds.2008.21.221

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

Received  February 2007 Revised  September 2007 Published  February 2008

Let us consider the problem

$-\Delta u+a(|x|)u=\lambda e^u$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.

Citation: M. Grossi. Existence of radial solutions for an elliptic problem involving exponential nonlinearities. Discrete & Continuous Dynamical Systems - A, 2008, 21 (1) : 221-232. doi: 10.3934/dcds.2008.21.221
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