3 papers
math.AP2026
Normalized solutions of quasilinear Schrödinger equations in the general -supercritical case
Qiang Gao, Xiaoyan Zhang
This paper is devoted to studying the existence of normalized solutions for the following quasilinear Schrödinger equation \begin{equation*} \begin{aligned} -Δu-uΔu^2 +λu=h(u) \qua…
math.AP2025
Ground state and multiple normalized solutions of quasilinear Schrödinger equations in the -supercritical case and the Sobolev critical case
Qiang Gao, Xiaoyan Zhang
This paper is devoted to studying the existence of normalized solutions for the following quasilinear Schrödinger equation \begin{equation*} \begin{aligned} -Δu-uΔu^2 +λu=|u|^{p-2}…
math.AP2024
Normalized ground state solutions of Schrödinger-KdV system in
Qian Gao, Qun Wang, Xiaojun Chang
In this paper, we study the coupled Schrödinger-KdV system \begin{align*} \begin{cases} -Δu +λ_1 u=u^3+βuv~~&\text{in}~~\mathbb{R}^{3}, \\-Δv +λ_2 v=\frac{1}{2}v^2+\frac{1}{2}βu^2~…