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arXiv · 2602.16506

Fully sign-changing Nehari constraint vs sign-changing solutions of a competitive Schr\"{o}dinger system

Xuejiao Fu·Fukun Zhao
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Abstract

We study a competitive nonlinear Schr\"odinger 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 $q\in [1,\infty]$.

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Xuejiao Fu, Fukun Zhao. 2026-02-18. Fully sign-changing Nehari constraint vs sign-changing solutions of a competitive Schr\"{o}dinger system. https://arxiv.org/abs/2602.16506

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