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pro vyhledávání: '"locally finite graphs"'
In this paper, we first define a discrete version of the fractional Laplace operator $(-\Delta)^{s}$ through the heat semigroup on a stochastically complete, connected, locally finite graph $G = (V, E, \mu, w)$. Secondly, we define the fractional div
Externí odkaz:
http://arxiv.org/abs/2408.02902
Publikováno v:
Boundary Value Problems, (2024)2024:134
By using the well-known mountain pass theorem and Ekeland's variational principle, we prove that there exist at least two fully-non-trivial solutions for a $(p,q)$-Kirchhoff elliptic system with the Dirichlet boundary conditions and perturbation term
Externí odkaz:
http://arxiv.org/abs/2408.02041
Autor:
Hu, Yuanyang, Wang, Mingxin
Let $G=(V,E)$ be a locally finite connected graph. We develop the first eigenvalue method on $G$ introduced in 1963 by Kaplan \cite{Kaplan} on Euclidean space, the discrete Phragm\'{e}n-Lindel\"{o}f principle of parabolic equations and upper and lowe
Externí odkaz:
http://arxiv.org/abs/2405.18173
We study the Localization game on locally finite graphs trees, where each of the countably many vertices have finite degree. In contrast to the finite case, we construct a locally finite tree with localization number $n$ for any choice of positive in
Externí odkaz:
http://arxiv.org/abs/2404.02409
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Akademický článek
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Autor:
Yang, Ping, Zhang, Xingyong
We investigate the existence of two nontrivial solutions for a poly-Laplacian system involving concave-convex nonlinearities and parameters with Dirichlet boundary condition on locally finite graphs. By using the mountain pass theorem and Ekeland's v
Externí odkaz:
http://arxiv.org/abs/2308.07584
In this paper, we develop the theory of Sobolev spaces on locally finite graphs, including completeness, reflexivity, separability, and Sobolev inequalities. Since there is no exact concept of dimension on graphs, classical methods that work on Eucli
Externí odkaz:
http://arxiv.org/abs/2306.02262
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+
Externí odkaz:
http://arxiv.org/abs/2310.07508
We are mainly concerned with the nonlinear $p$-Laplace equation \begin{equation*} -\Delta_pu+\rho|u|^{p-2}u=\psi(x,u) \end{equation*} on a locally finite graph $G=(V,E)$, where $p$ belongs to $(1, +\infty)$. We obtain existence of positive solutions
Externí odkaz:
http://arxiv.org/abs/2306.14121