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A local min-orthogonal method for multiple solutions of strongly coupled elliptic systems

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  • The aim of this paper is to numerically investigate multiple solutions of semilinear elliptic systems with zero Dirichlet boundary conditions

    -$\Delta u=F_u(x;u,v),$   $x\in\Omega,
    -$\Delta v=F_v(x;u,v),$   $x\in\Omega,

    where $\Omega \subset \mathbb{R}^{N}$ ($N\ge 1$) is a bounded domain. A strongly coupled case where the potential $F(x;u,v)$ takes the form $|u|^{\alpha_1}|v|^{\alpha_2}$ with $\alpha_1, \alpha_2>1$ is specially studied. By using a local min-orthogonal method, both positive and sign-changing solutions are found and displayed.

    Mathematics Subject Classification: Primary: 35A40, 35A15; Secondary: 58E05.


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