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 $\Omega \subset\subset \mathbb{R}^{2l}$ where $2l$ is the order of the equation. Considered are the problem with no symmetry requirements on the domain, the radial problem on an annulus, and the radial problem on a ball with a Hardy potential term.