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math.AP2026
Uniqueness of positive solutions of double-power nonlinear stationary Schrödinger equations: the fixed frequency case and the fixed mass case
Linjie Song, Wenming Zou
The existence of a positive radial solution to the problem \begin{align*} -Δu + λu = u^p + u^q, \quad u \in H^1(\mathbb{R}^N), ~~ N \ge 2, \end{align*} where and $1 < q < p…
math.AP2026
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…
math.AP2024
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…