Nodal solutions of a NLS equation concentrating on lower dimensional spheres

非紧度量图上的常号与变号NLS基态

Constant sign and sign changing NLS ground states on noncompact metric graphs

本文研究非紧度量图上非线性薛定谔方程基态与节点基态的存在性，给出基于无穷远水平的充分条件，并针对有限边与无限边图类获得尖锐的拓扑与度量判据，揭示图与欧氏空间节点结构的本质差异。

{Localized nodal solutions for $p-$Laplacian equations with critical exponents in $\mathbb{R}^N$

In this paper, we consider the existence of localized sign-changing solutions for the $p-$Laplacian nonlinear Schrödinger equation $$ -ε^pΔ_pu+V(x)|u|^{p-2}u=|u|^{p^*-2}u+μ|u|^{q-2}u,~~u\in W^{1,p}(\mathbb{R}^N), $$ where $1<p<N$, $p_N=\max\{p,p^*-1\}<q<p^*=\frac{Np}{N-p}$, $μ>0$, $Δ_p$ is the $p-$Laplacian operator. By using the penalization method together with the truncation method and a blow-up argument, we establish for small $ε$ the existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function.

平面倍增节点解与Yamabe方程的最大秩

Planar doubling nodal solutions to the Yamabe equation with maximal rank

本文构造了两个Yamabe方程的节点解家族，每个解在两个平面圆上集中。其中一族与Medina-Musso之前结果一致，另一族为新变种，基于非Kelvin对称的假设。在三维情况下，这些解达到最大秩，通过连续的共形变换分析两圆相互作用，表现出类似涡旋动力学中的跃迁行为。

NLS方程在L²约束下的渐近球体集中于无穷远

Asymptotic Sphere Concentration at Infinity for NLS with L^2 Constraint

研究NLS方程在L²约束下的高维球体在无穷远处的集中现象，通过定制约简和吹胀分析扩展了二维质量临界结果。

具有部分约束的非线性 Schrödinger 方程的多解

Multiple solutions to the nonlinear Schrödinger equation with a partial confinement

本文研究带部分约束的 NLS 多解，证明正基态存在、最低能量变号解不存在，并发现原点相交的鞍点型节点解及相应对称性质。