Existence and convergence of solutions for nonlinear elliptic systems on graphs

arXiv2111.11078MaRDI QIDQ6383618

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Publication date: 22 November 2021

Abstract: We consider a kind of nonlinear systems on a locally finite graphs $G=(V,E)$. We prove via the mountain pass theorem that this kind of systems has a nontrivial ground state solution which depends on the parameter $lambda$ with some suitable assumptions on the potentials. Moreover, we pay attention to the concentration behavior of these solutions and prove that, as $lambdaoinfty$, these solutions converge to a ground state solution of a corresponding Dirichlet problem. Finally, we also provide some numerical experiments to illustrate our results.

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