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We prove the existence of infinitely many solutions to a class ofnon-symmetric Dirichlet problems with exponential nonlinearities. Here thedomain $\Omega \subset\subset \mathbb{R}^{2l}$ where $2l$ is the order of theequation. Considered are the problem with no symmetry requirements on thedomain, the radial problem on an annulus, and the radial problem on a ball witha Hardy potential term.

Multiplicity of solutions for polyharmonic Dirichlet problems with exponential nonlinearities and broken symmetry