MULTIPLE SOLUTIONS OF SOME ELLIPTIC SYSTEMS WITH LINEAR COUPLINGS

doi:10.1007/s10473-021-0408-6

Abstract

Abstract: 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.

Key words: Morse theory, multiplicity, elliptic system, linear couplings

CLC Number:

37B30

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.

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