Electron. J. Diff. Equ., Vol. 2013 (2013), No. 181, pp. 1-22.

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

Haining Fan, Xiaochun Liu

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 7, 2013.
Math Subject Classifications: 35J20, 58J05.
Key Words: Nehari manifold; critical cone Sobolev exponent; totally characteristic degeneracy; sign-changing weight function.

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Haining Fan
School of Mathematics and Statistics, Wuhan University
Wuhan 430072, China
email:fanhaining888@163.com
  Xiaochun Liu
School of Mathematics and Statistics, Wuhan University
Wuhan 430072, China
email: xcliu@whu.edu.cn

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