3 papers
math.AP2026
Normalized solutions for a class of gradient-type Schrödinger systems under Neumann boundary conditions in bounded domains
Xiaojun Chang, Yuxin Li, Yohei Sato +1
We investigate the existence of normalized solutions to the gradient-type Schrödinger system \begin{equation*} \begin{cases} -Δu+ V_1(x)u+λu= uv^2 & \text{ in } Ω,\\ -Δv+ V_2(x)v+λ…
math.AP2026
Existence of Kelvin-Invariant Positive Solutions for Critical Elliptic Equations with Variable Coefficients via Profile Decomposition
Yohei Sato, Reo Suzuki
In this paper, we consider the following critical nonlinear elliptic equation: \[ - Δu = a(x) |u|^{2^*-2}u \quad \text{in } \mathbb{R}^N, \quad u \in \mathcal{D}^{1,2}(\mathbb{R}^N…
math.AP2026
On the existence of vector solutions to nonlinear Schrödinger equations with weak three-wave interaction
T. Kinoshita, Y. Sato
We study a nonlinear Schrödinger system with three-wave interaction: \begin{equation*} \left\{\begin{aligned} & - Δu_1 = f_1(u_1) + αu_2u_3 \quad \text{ in } \R^N, & - Δu_2 = f_2(u…