| Abstract: |
| In this talk, we present a variational approach to semilinear elliptic problems with exponential nonlinearities in (possibly unbounded) annular domains of $\R^N$. These problems present significant analytical difficulties in dimensions $N \geq 3$, where the classical Sobolev framework is not sufficient to handle nonlinear terms with exponential growth. To overcome these difficulties, we combine tools from Orlicz space theory (which provide a natural functional setting to handle non-polynomial nonlinearities) with nonsmooth critical point methods in the spirit of Szulkin. This approach allows us to recover a suitable variational structure despite the lack of standard compactness properties. Under suitable structural assumptions, we establish the existence of positive solutions that are not radially symmetric, thereby exhibiting symmetry-breaking phenomena for this class of elliptic problems. |
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