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 in [Nonlinear Anal. 22 (1994), 277-293].