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arXiv · 1902.02150

Entire nodal solutions to the critical Lane-Emden system

Mónica Clapp·Alberto Saldaña
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Abstract

We establish the existence of finitely many sign-changing solutions to the Lane-Emden system $$-\Delta u=|v|^{q-2}v,\quad -\Delta v=|u|^{p-2}u \quad \text{ in }\mathbb{R}^N, \ \ N\geq 4,$$ where the exponents $p$ and $q$ lie on the critical hyperbola $\frac{1}{p}+\frac{1}{q}=\frac{N-2}{N}$. These solutions are nonradial and arise as limit profiles of symmetric sign-changing minimizing sequences for a critical higher-order problem in a bounded domain.

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Mónica Clapp, Alberto Saldaña. 2019-02-06. Entire nodal solutions to the critical Lane-Emden system. https://arxiv.org/abs/1902.02150

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