Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 181, pp. 1-22.

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

Authors: Haining Fan  (Wuhan Univ., Wuhan, China)
         Xiaochun Liu (Wuhan Univ., Wuhan, China)

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.

Submitted March 19, 2013. Published August 07, 2013.
Math Subject Classifications: 35J20, 58J05.
Key Words: Nehari manifold; critical cone Sobolev exponent; 
           totally characteristic degeneracy; sign-changing weight function.