In this paper, we study the existence of nontrivial solutions to the elliptic system \begin{equation*} \begin{cases} -\Delta u=\lambda v + F_u(x,u,v),& \ x\in\Omega,\\ -\Delta v=\lambda u + F_v(x,u,v),& \ x\in\Omega,\\ u=v=0,& \ x\in\partial\Omega, \end{cases} \end{equation*} where $\Omega\subset\mathbb{R}^N$ is bounded with a smooth boundary. By the Morse theory and the Gromoll-Meyer pair, we obtain multiple nontrivial vector solutions to this system.
Yutong CHEN
,
Jiabao SU
,
Mingzheng SUN
,
Rushun TIAN
. MULTIPLE SOLUTIONS OF SOME ELLIPTIC SYSTEMS WITH LINEAR COUPLINGS[J]. Acta mathematica scientia, Series B, 2021
, 41(4)
: 1141
-1150
.
DOI: 10.1007/s10473-021-0408-6
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