Multiple solutions for a polyharmonic homogeneous boundary value problem with critical exponent

Abstract

In this paper, we analyse the polyharmonic equation in a bounded smooth domain with homogeneous Dirichlet conditions on the boundary and critical exponents. We will obtain a relationship between the topological domain and the multiplicity of solutions. We also give symmetry properties of the solutions and a result about breaking symmetry.

Keywords:

• Polyharmonic operator
• critical exponent
• multiple solutions

AMS Subject Classifications:

• 31B30
• 35B33
• 35J30

Acknowledgements

We are indebted to the Referee for very careful reading and many valuable suggestions and comments.

Notes

No potential conflict of interest was reported by the authors.