4 papers · 1 filter
Exact number of positive solutions and existence of sign-changing solutions with prescribed mass for NLS on bounded domains
Linjie Song, Wenming Zou
Given , we study the elliptic problem: \begin{align*} \text{ find } (u,λ) \in H_0^1(Ω) \times \mathbb{R} \text{ such that } -Δu + λu = |u|^{p-2}u \text{ in } Ω\text{ and } \i…
Multiple sign-changing and semi-nodal normalized solutions for a Gross-Pitaevskii type system on bounded domains: the -supercritical case
Tianhao Liu, Linjie Song, Qiaoran Wu +1
In this paper we investigate the existence of multiple sign-changing and semi-nodal normalized solutions for an -coupled elliptic system of the Gross-Pitaevskii type: \begin{equ…
Two Positive Normalized Solutions on Star-shaped Bounded Domains to the Brézis-Nirenberg Problem, I: Existence
Linjie Song, Wenming Zou
We develop a new framework to prove the existence of two positive solutions with prescribed mass on star-shaped bounded domains: one is the normalized ground state and another is o…
Two Positive Normalized Solutions and Phase Separation for Coupled Schrödinger Equations on Bounded Domain with L2-Supercritical and Sobolev Critical or Subcritical Exponent
Linjie Song, Wenming Zou
In this paper we study the existence of positive normalized solutions of the following coupled Schrödinger system: \begin{align} \left\{ \begin{aligned} & -Δu = λ_u u + μ_1 u^3 + β…