Ambrosio, L. and Cabre, X. (2000) Entire Solution of Semilinear Elliptic Equations in R3 and a Conjecture of De Giorgi. Journal of the American Mathematical Society, 13, 725-739. http://dx.doi.org/10.1090/S0894-0347-00-00345-3

has been cited by the following article:

• 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.