On the least energy sign-changing solutions for a nonlinear elliptic system

Yohei Sato; Zhi-Qiang Wang

doi:10.3934/dcds.2015.35.2151

Article Contents

2015, Volume 35, Issue 5: 2151-2164. Doi: 10.3934/dcds.2015.35.2151

This issue Previous Article Local integration by parts and Pohozaev identities for higher order fractional Laplacians Next Article Random backward iteration algorithm for Julia sets of rational semigroups

On the least energy sign-changing solutions for a nonlinear elliptic system

Yohei Sato^1, and
Zhi-Qiang Wang^2,

1.
Osaka City University Advanced Mathematical Institute, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Smiyoshi-ku, Osaka 558-8585
2.
Chern Institute Mathematics and LPMC, Nankai University, Tianjin 300071

Received: July 31, 2013

Revised: August 31, 2014

Published: May 2017

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Abstract

In this paper, as bound state solutions we consider least energy sign-changing solutions to a nonlinear elliptic system which consists of N-equations defined on a bounded domain $\Omega$. For any subset $K\subset \{1,\cdots, N\}$, we show the existence of sign-changing solution $\vec{u}=(u_1,\cdots,u_n)$ such that, for $i\in K$, $u_i$ are sign-changing functions that change sign exactly once in $\Omega$, and, for $i\notin K$, $u_i$ are one sign functions. We give a variational characterization of such solutions on modified Nehari type constrained sets.

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Mathematics Subject Classification: Primary: 35J50; Secondary: 47J30.

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