On G-invariant solutions of a singular biharmonic elliptic system involving multiple critical exponents in RN $R^{N}$

Abstract

Abstract In this work, a biharmonic elliptic system is investigated in RN $\mathbb{R}^{N}$, which involves singular potentials and multiple critical exponents. By the Rellich inequality and the symmetric criticality principle, the existence and multiplicity of G-invariant solutions to the system are established. To our best knowledge, our results are new even in the scalar cases.

Keywords

• G-invariant solution
• Rellich inequality
• Symmetric criticality principle
• Biharmonic elliptic system