Multiplicity of solutions to the sum of polyharmonic equations with critical Sobolev exponents

Abstract

In this article, we prove multiplicity of solutions for the sum of polyharmonic equation with critical Sobolev exponent. The proof is based upon the methods of weakly lower semi-continuous of the functionals and the Mountain Pass Lemma without (PS) conditions.

Keywords

• Polyharmonic equation
• multiple solutions
• critical Sobolev exponent