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Existence of nodal solution for semi-linear elliptic equations with critical sobolev exponent on singular manifold
LIU Xiao-Chun #,MEI Yuan
School of Mathematics and Statistics,Wuhan University, Wuhan 430072
*Correspondence author
#Submitted by
Subject:
Funding: NSFC （No. 11171261）, RFDP （No. 200804860046）
Opened online:19 November 2012
Accepted by: none
Citation: LIU Xiao-Chun,MEI Yuan.Existence of nodal solution for semi-linear elliptic equations with critical sobolev exponent on singular manifold[OL]. [19 November 2012] http://en.paper.edu.cn/en_releasepaper/content/4494743
 
 
In this paper we will introduce the manifolds with conical singularities,the cone Sobolev spaces and the corresponding cone Sobolev inequality and Poincar'{e} inequality for the weighted cone Sobolev spaces.we prove that semi-linear elliptic equations with critical cone Sobolev exponents on manifolds with cone sigularites possess a nodal solution in cone Sobolev spaces.The main mehtod is to define the energy functional of the equation and the corresponding Nehari sets for nodal solution and estimate them.
Keywords:cone Sobolev space; critical exponent; nodal solution
 
 
 

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