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- W2952100863 abstract "We consider the nonlinear Schr{o}dinger equation $-Delta u+(lambda a(x)+1)u=|u|^{p-1}u$ on a locally finite graph $G=(V,E)$. We prove via the Nehari method that if $a(x)$ satisfies certain assumptions, for any $lambda>1$, the equation admits a ground state solution $u_lambda$. Moreover, as $lambdarightarrow infty$, the solution $u_lambda$ converges to a solution of the Dirichlet problem $-Delta u+u=|u|^{p-1}u$ which is defined on the potential well $Omega$. We also provide a numerical experiment which solves the equation on a finite graph to illustrate our results." @default.
- W2952100863 created "2019-06-27" @default.
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- W2952100863 date "2017-05-10" @default.
- W2952100863 modified "2023-09-26" @default.
- W2952100863 title "Convergence of ground state solutions for nonlinear Schr{o}dinger equations on graphs" @default.
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- W2952100863 doi "https://doi.org/10.48550/arxiv.1705.03981" @default.
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