# American Institute of Mathematical Sciences

May  2015, 35(5): 2151-2164. doi: 10.3934/dcds.2015.35.2151

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

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

Received  August 2013 Revised  September 2014 Published  December 2014

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.
Citation: Yohei Sato, Zhi-Qiang Wang. On the least energy sign-changing solutions for a nonlinear elliptic system. Discrete & Continuous Dynamical Systems, 2015, 35 (5) : 2151-2164. doi: 10.3934/dcds.2015.35.2151
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