Minimizers of $L^2$-Subcritical Inhomogeneous Variational Problems with A Spatially Decaying Nonlinearity

Abstract

We study the minimizers of $L^2$-subcritical inhomogeneous variational problems with spatially decaying nonlinear terms, which contain $x = 0$ as a singular point. The limit concentration behavior of minimizers is proved as $M\to\infty$ by establishing the refined analysis of the spatially decaying nonlinear term.