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

DOI: 10.4236/apm.2014.44017   PDF   HTML   XML   3,734 Downloads   5,419 Views  

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.

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Liu, Y. and Wang, J. (2014) Nondegeneracy of Solution to the Allen-Cahn Equation with Regular Triangle Symmetry. Advances in Pure Mathematics, 4, 103-107. doi: 10.4236/apm.2014.44017.

Conflicts of Interest

The authors declare no conflicts of interest.

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