Exact number of positive solutions and existence of sign-changing solutions with prescribed mass for NLS on bounded domains

Linjie Song, Wenming Zou

Given $\hat{I}¼>0$, 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{ an…