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

TL;DR

This paper establishes the existence of infinitely many solutions for non-symmetric polyharmonic Dirichlet problems with exponential nonlinearities, covering various domain symmetries and including Hardy potential considerations.

Contribution

It extends the theory by proving multiple solutions for complex polyharmonic problems without symmetry constraints, including radial cases and Hardy potential effects.

Findings

Infinitely many solutions exist for the considered problems.

Solutions are obtained without symmetry assumptions on the domain.

Results include radial problems with Hardy potential.

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.