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

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