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| We study the following semilinear elliptic problem
\[\left\{ \begin{array}{ll}
-\Delta u+mu= |u|^{p-2}u +f(x) & \text{in }\Omega ={\mathbb R}^{N}\setminus B_{R} \\
u=\xi & \text{on }\partial \Omega =\partial B_{R} \\
u\rightarrow 0 & \text{as } |x| \rightarrow +\infty ,
\end{array}\right. \]
where $m>0$, $N\geq 3$, $\xi \in {\mathbb R}$ and $p > 2$ but subcritical.
If $f:\Omega \rightarrow {\mathbb R}$ is a radial function, we prove the existence of infinitely many radial solutions by using variational tools, perturbative methods and suitable growth estimates on min-max critical levels.
No restriction on the exponent $p$ is required for $N$ large enough.
Joint work with Sara Barile. |
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