## Topological Methods in Nonlinear Analysis

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

Edger Sterjo

#### 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].

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 50, Number 1 (2017), 27-63.

Dates
First available in Project Euclid: 14 October 2017

https://projecteuclid.org/euclid.tmna/1507946570

Digital Object Identifier
doi:10.12775/TMNA.2017.018

Mathematical Reviews number (MathSciNet)
MR3706151

Zentralblatt MATH identifier
06850990

#### Citation

Sterjo, Edger. Multiplicity of solutions for polyharmonic Dirichlet problems with exponential nonlinearities and broken symmetry. Topol. Methods Nonlinear Anal. 50 (2017), no. 1, 27--63. doi:10.12775/TMNA.2017.018. https://projecteuclid.org/euclid.tmna/1507946570

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