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Alessio, F., Calamai, A. and Montecchiari, P. (2007) Saddle-Type Solutions for a Class of Semilinear Elliptic Equations. Advances in Differential Equations, 12, 361-380.

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• 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.