The existence of extremal functions for discrete Sobolev inequalities on lattice graphs

B Hua, R Li - Journal of Differential Equations, 2021 - Elsevier
In this paper, we study the existence of extremal functions (pairs) of the following discrete
Sobolev inequality (0.1) and Hardy-Littlewood-Sobolev inequality (0.2) in the lattice …

A Liouville theorem for elliptic equations with a potential on infinite graphs

S Biagi, G Meglioli, F Punzo - Calculus of Variations and Partial Differential …, 2024 - Springer
We investigate the validity of the Liouville property for a class of elliptic equations with a
potential, posed on infinite graphs. Under suitable assumptions on the graph and on the …

The generalized porous medium equation on graphs: existence and uniqueness of solutions with data

D Bianchi, AG Setti, RK Wojciechowski - Calculus of Variations and Partial …, 2022 - Springer
We study solutions of the generalized porous medium equation on infinite graphs. For
nonnegative or nonpositive integrable data, we prove the existence and uniqueness of mild …

The Kazdan–Warner equation on canonically compactifiable graphs

M Keller, M Schwarz - Calculus of Variations and Partial Differential …, 2018 - Springer
The Kazdan–Warner equation on canonically compactifiable graphs | SpringerLink Skip to
main content Advertisement SpringerLink Log in Menu Find a journal Publish with us Search …

A non-local quasi-linear ground state representation and criticality theory

F Fischer - Calculus of Variations and Partial Differential …, 2023 - Springer
We study energy functionals associated with quasi-linear Schrödinger operators on infinite
weighted graphs, and develop a ground state representation. Using the representation, we …

The th Kazdan–Warner equation on graphs

H Ge - Communications in Contemporary Mathematics, 2020 - World Scientific
Let G=(V, E) be a connected finite graph and C (V) be the set of functions defined on V. Let Δ
p be the discrete p-Laplacian on G with p> 1 and L= Δ p− k, where k∈ C (V) is positive …

Uniqueness in weighted spaces for the Schr\"odinger equation on infinite graphs

G Meglioli, F Punzo - arxiv preprint arxiv:2212.05928, 2022 - arxiv.org
arxiv:2212.05928v2 [math.AP] 4 Jan 2023 Page 1 arxiv:2212.05928v2 [math.AP] 4 Jan
2023 UNIQUENESS IN WEIGHTED lp SPACES FOR THE SCHRODINGER EQUATION ON …

Blow-up and global existence for semilinear parabolic equations on infinite graphs

G Grillo, G Meglioli, F Punzo - arxiv preprint arxiv:2406.15069, 2024 - arxiv.org
We investigate existence of global in time solutions and blow-up of solutions to the
semilinear heat equation posed on infinite graphs. The source term is a general function $ f …

General Cheeger inequalities for p-Laplacians on graphs

M Keller, D Mugnolo - Nonlinear Analysis: Theory, Methods & Applications, 2016 - Elsevier
We prove Cheeger inequalities for p-Laplacians on finite and infinite weighted graphs.
Unlike in previous works, we do not impose boundedness of the vertex degree, nor do we …

The wave equation on lattices and oscillatory integrals

C Bi, J Cheng, B Hua - arxiv preprint arxiv:2312.04130, 2023 - arxiv.org
In this paper, we establish sharp dispersive estimates for the linear wave equation on the
lattice $\mathbb {Z}^ d $ with dimension $ d= 4$. Combining the singularity theory with …