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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.16384 |
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Table of Contents:
- We investigate in this work families $(u_ε)_{ε>0}$ of sign-changing blowing-up solutions of asymptotically critical stationary nonlinear Schrödinger equations of the following type: $$Δ_g u_ε+ h_εu_ε= |u_ε|^{p_ε-2} u_ε$$ in a closed manifold $(M,g)$, where $h_ε$ converges to $h$ in $C^1(M)$. Assuming that $(u_ε)_{ε>0}$ blows-up as \emph{a single sign-changing bubble}, we obtain necessary conditions for blow-up that constrain the localisation of blow-up points and exhibit a strong interaction between $h$, the geometry of $(M,g)$ and the bubble itself. These conditions are new and are a consequence of the sign-changing nature of $u_ε$.