### A Note on Calculation of Asymptotic Energy for a Functional of Ginzburg-Landau Type with Externally Imposed Lower-Order Oscillatory Term in One Dimension

In this note we consider the Ginzburg-Landau functional $${I}_{a}^{\u03f5}(v)={\int}_{0}^{1}({\u03f5}^{2}{v}^{\mathrm{\prime \prime}2}(s)+W({v}^{\prime}(s))+a({\u03f5}^{-\beta}s({v}^{2}(s))ds$$ where $\beta >0$ and a is 1-periodic. We determine how (rescaled) minimal asymptotic energy associated to ${I}_{a}^{\u03f5}$ depends on parameter $\beta >0$ as $\u03f5\xf80$. In particular, our analysis shows that minimizers of ${I}_{a}^{\u03f5}$ are nearly ${\u03f5}^{1/3}$-periodic.