Some properties of asymptotic energy of a class of functionals of Ginzburg-Landau type endowed with generalized lower-order oscillatory term in one dimension

We consider a generalization of the functional of Ginzburg-Landau type studied in the paper A. Raguž: A note on calculation of asymptotic energy for Ginzburg-Landau functional with externally imposed lower-order oscillatory term in one dimension, Boll. Un. Mat. Ital. (8)10-B , 1125-1142 (2007), whereby the oscillatory term a(ε^−βs) (where a ∈ L¹_per(0, 1) and β > 0) is replaced by a(ρ_εs) (where lim_ε−→0 ρ_ε = +∞). We describe how the expression for the rescaled asymptotic energy of such class of functionals depends on the properties of the sequence (ρ_ε). (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)