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Nondegeneracy of Solution to the Allen-Cahn Equation with Regular Triangle Symmetry
Department of Mathematics and Physics, North China Electric Power University, Beijing, China
Department of Mathematics and Physics, North China Electric Power University, Beijing, China
- 1 Department of Mathematics and Physics, North China Electric Power University, Beijing, China
- 2 Department of Mathematics and Physics, North China Electric Power University, Beijing, China
Advances in Pure Mathematics·Volume 04 (2014)·Pages 103–107·Published 9 April 2014·DOI10.4236/apm.2014.44017
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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 .
KeywordsAllen-Cahn EquationMultiple-End SolutionNondegeneracy
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