Normalized multibump solutions to nonlinear Schrödinger equations with steep potential well

We are concerned with the existence of multibump solutions to the nonlinear Schrödinger equation −Δu+λa(x)u+μu=|u|2σuinRN with an L 2-constraint ‖u‖L2(RN)2=ρ in the L 2-subcritical case σ ∈ (0, 2/N) and the L 2-supercritical case σ ∈ (2/N, 2*/N), where th

我们关注非线性薛定谔方程\(-\Delta u + \lambda a(x)u + \mu u = |u|^{2\sigma}u\)在\(\mathbb{R}^N\)中，在\(L^2\)约束\(\|u\|_{L^2(\mathbb{R}^N)}^2 = \rho\)下的多峰解的存在性，其中包括\(L^2\)次临界情形\(\sigma \in (0, \frac{2}{N})\)和\(L^2\)超临界情形\(\sigma \in (\frac{2}{N}, \frac{2^*}{N})\)，这里（最后一个单词“where th”似乎不完整，可能影响对整体内容更准确的理解）