%0 Journal Article
%T Nondegeneracy of Solution to the Allen-Cahn Equation with Regular Triangle Symmetry
%A Yong Liu
%A Jun Wang
%J Advances in Pure Mathematics
%P 103-107
%@ 2160-0384
%D 2014
%I Scientific Research Publishing
%R 10.4236/apm.2014.44017
%X <p class=\"MsoNormal\" style=\"text-align:justify;\">
	<span lang=\"EN-US\"><span style=\"font-family:Verdana;\">The
Allen-Cahn equation on the plane has a 6-end solution <em>U</em> with regular triangle
symmetry. The angle between consecutive nodal lines of <em>U</em> is <img src=\"Edit_c289fc92-df64-4f64-a985-1eed29e6313d.bmp\" alt=\"\" height=\"15\" width=\"21\" /></span></span><span lang=\"EN-US\"><span style=\"font-family:Verdana;\">. We prove in this paper
that <em>U</em> is non-degenerated in the class of functions possessing regular
triangle symmetry. As an application, we show the existence of a family of
solutions close to <em>U</em>.</span></span> 
</p>
%K Allen-Cahn Equation
%K Multiple-End Solution
%K Nondegeneracy
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=44634