Stable and finite Morse index solutions on Rn or on bounded domains with small diffusion, II

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Finite Morse index solutions of an elliptic equation with supercritical exponent (2011, background): “Recently, significant progress has been made along this line of research by Dancer [3–6] and Farina [12].”
Symmetry of Solutions to Variational Problems for Nonlinear Elliptic Equations via Reflection Methods (2010, background): “Another motivation comes from boundary value problems with small diffusion as discussed in [ 35 , 36], where an asymptotic description of the shape of solutions with finite Morse index is of interest.”
MULTIPLE-END SOLUTIONS TO THE ALLEN-CAHN EQUATION IN R2 (2010, background): “We recall here that the heteroclinic is stable, and from [5] we know that in dimension N = 2 stability of a solution implies that it is necessarily a one dimensional solution (for the related minimality conjecture, see for example [28] and [26] and the reference therein).”
Entire solutions of the Allen-Cahn equation and complete embedded minimal surfaces. (2009, background): “[7] E. N. Dancer, Stable and finite Morse index solutions on Rn or on bounded domains with small diffusion.”