Nondegeneracy of Solution to the Allen-Cahn Equation with Regular Triangle Symmetry

Yong Liu, Jun Wang

Department of Mathematics and Physics, North China Electric Power University, Beijing, China.

DOI: 10.4236/apm.2014.44017                

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.

Keywords

Allen-Cahn Equation, Multiple-End Solution, Nondegeneracy

Conflicts of Interest

The authors declare no conflicts of interest.

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