Multiple solutions to singular fourth order elliptic equations on compact manifolds

Abstract

Using the method of Nehari manifolds, we prove the existence of at least two distinct weak solutions to elliptic equation of four order with singularities and with critical Sobolev growth.

Keywords:

• singular fourth order elliptic equation
• Hardy inequality
• Sobolev’s exponent growth
• Nehari manifold

AMS Subject Classification:

• 58J05

Acknowledgements

The authors are thankful to the referee for valuable suggestions towards the improvement of this paper.