TITLE:
Nondegeneracy of Solution to the Allen-Cahn Equation with Regular Triangle Symmetry
AUTHORS:
Yong Liu, Jun Wang
KEYWORDS:
Allen-Cahn Equation, Multiple-End Solution, Nondegeneracy
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.4 No.4,
April
9,
2014
ABSTRACT: The
Allen-Cahn equation on the plane has a 6-end solution U with regular triangle
symmetry. The angle between consecutive nodal lines of U is . We prove in this paper
that U 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 U.