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- W4387596411 abstract "Suppose that $G=(V, E)$ be a locally finite and connected graph with symmetric weight and uniformly positive measure, where $V$ denotes the vertex set and $E$ denotes the edge set. We are concered with the following problem $$ begin{cases}-Delta u+h u=f(x, u), & text { in } Omega, u=0, & text { on } partial Omega,end{cases} $$ on the graph, where $h: Omega rightarrow mathbb{R}$, $f: Omega times mathbb{R} rightarrow mathbb{R}$ and $u: Omega rightarrow mathbb{R}$. When $ f $ and $ h $ satisfies certain assumption conditions, we can ascertain the existence of one or two nontrivial solutions on the graph." @default.
- W4387596411 created "2023-10-13" @default.
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- W4387596411 date "2023-10-11" @default.
- W4387596411 modified "2023-10-14" @default.
- W4387596411 title "Existence of Nontrivial Solutions for the Nonlinear Equation on Locally Finite Graphs" @default.
- W4387596411 doi "https://doi.org/10.48550/arxiv.2310.07508" @default.
- W4387596411 hasPublicationYear "2023" @default.
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