2020 Mathematics Subject Classification. Primary: 35Q40, 46N50; Secondary: 35J20. Key words and phrases. L2-subcritical, spatially decaying nonlinearity, minimizers, energy estimates, mass concentration. The second author is partially supported by NSFC under Grants 12225106 and 11931012, as well as the Fundamental Research Funds for the Central Universities #CCNU22LJ002. ∗Corresponding author: Shuang Wu.