Concentration at curves for a singularly perturbed Neumann problem in three-dimensional domains

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On the number of interior peak solutions for a singularly perturbed Neumann problem (2007, unknown): “Theenergy functionalassociatedwith (1.5) is (1.9) ¬«¯® {û°² £ ³µ´ © v x ¶ ¸ { ¶ x ¹{ x ª } ³µ´7ü © { ª- { õ ¨ © Hª where ü © { ª Dý ó á ©Xþ ªÕÿ þ .”
Chapter 6 Existence and stability of spikes for the Gierer-Meinhardt system (2008, methodology): “Mathematical modeling of patterns in biological morphogenesis using extensions of GM model are discussed in [36] and [ 48 ].”
Some new entire solutions of semilinear elliptic equations on Rn (2009, result): “For problem (P"), in [43], [44] it has been proved that, given any n 2 N and any p > 1, there exist solutions concentrating at the whole boundary of › if " tends to zero along a suitable sequence "j, corresponding to k = n i 1. The result has been extended in [37], [ 41 ] for general k, and the limi”
Concentration on curves for nonlinear Schrödinger Equations (2007, background): “Recently in [ 27 , 26] this boundary concentration on a geodesic of the boundary in the 3d-case has been treated via arbitrarily high order approximations.”