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Existence and Convergence of Solutions for Nonlinear Elliptic Systems on Graphs by Xu, Jinyan; Zhao, Liang is a scholarly article available to read on EtoBox.

What is Existence and Convergence of Solutions for Nonlinear Elliptic Systems on Graphs about?

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 $\lambda \to \infty$, these solutions converge to a ground state solution of a corresponding Dirichlet problem. Finally, we also provide some numerical experiments to illustrate our results.

Author

Xu, Jinyan; Zhao, Liang

Published

2021

Language

EN