National Key RD Program [2023YFA1010002]; Fundamental Research Funds for the Central Universities [CCNU22LJ002]; NSFC [12171183]; Fundamental Research Funds for the Central Universities [KJ02072020-0319]; Graduate Education Innovation Funds at Central China Normal University in P. R. China [2023CXZZ009]
机构署名：
本校为第一且通讯机构
院系归属：
数学与统计学学院
摘要：
We revisit the following nonlinear Schrödinger equation
$$\begin{aligned} -\varepsilon ^2\Delta u+ V(x)u=u^{p},\quad u>0,\;\; u\in H^1({\mathbb {R}}^N), \end{aligned}$$
where
$$\varepsilon >0$$
is a small parameter,
$$N\ge 2$$
and
$$1
