Multiple positive solutions for degenerate elliptic equations with critical cone Sobolev exponents on singular manifolds

Abstract

In this article, we show the existence of multiple positive solutions to a class of degenerate elliptic equations involving critical cone Sobolev exponent and sign-changing weight function on singular manifolds with the help of category theory and the Nehari manifold method.

Keywords

• Nehari manifold
• critical cone Sobolev exponent
• totally characteristic degeneracy
• sign-changing weight function