Fully sign-changing Nehari constraint vs sign-changing solutions of a competitive Schrödinger system
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910026022518784 |
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| author | Fu, Xuejiao Zhao, Fukun |
| author_facet | Fu, Xuejiao Zhao, Fukun |
| contents | We study a competitive nonlinear Schrödinger system in $\mathbb{R}^N$ whose nonlinear potential is localized in small regions that shrink to isolated points. Within a variational framework based on a fully sign-changing Nehari constraint and Krasnosel'skii genus, we construct, for all $\varepsilon>0$, a sequence of sign-changing solutions with increasing and unbounded energies, and after suitable translations they converge to a sequence of sign-changing solutions of the associated limiting system as $\varepsilon\to 0$ in $H^1$-norm. Moreover, these sign-changing solutions concentrate around the prescribed attraction points both in $H^1$-norm and $L^q$-norm for $q\in [1,\infty]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16506 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fully sign-changing Nehari constraint vs sign-changing solutions of a competitive Schrödinger system Fu, Xuejiao Zhao, Fukun Analysis of PDEs 35B44, 35B40, 35B20, 35J50 We study a competitive nonlinear Schrödinger system in $\mathbb{R}^N$ whose nonlinear potential is localized in small regions that shrink to isolated points. Within a variational framework based on a fully sign-changing Nehari constraint and Krasnosel'skii genus, we construct, for all $\varepsilon>0$, a sequence of sign-changing solutions with increasing and unbounded energies, and after suitable translations they converge to a sequence of sign-changing solutions of the associated limiting system as $\varepsilon\to 0$ in $H^1$-norm. Moreover, these sign-changing solutions concentrate around the prescribed attraction points both in $H^1$-norm and $L^q$-norm for $q\in [1,\infty]$. |
| title | Fully sign-changing Nehari constraint vs sign-changing solutions of a competitive Schrödinger system |
| topic | Analysis of PDEs 35B44, 35B40, 35B20, 35J50 |
| url | https://arxiv.org/abs/2602.16506 |