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

#### Abstract

We prove the existence of infinitely many solutions to a class of non-symmetric Dirichlet problems with exponential nonlinearities. Here the domain $\Omega \Subset \mathbb{R}^{2l}$ where $2l$ is also the order of the equation. Considered are the problem with no symmetry requirements, the radial problem on an annulus, and the radial problem on a ball with a Hardy potential term of critical Hardy exponent. These generalize results obtained by Sugimura \cite{Sugimura94}.

#### Keywords

Polyharmonic Dirichlet problems; perturbation from symmetry; critical point theory; variational methods

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