The existence of extremal functions for discrete Sobolev inequalities on lattice graphs
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 …
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
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 …
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
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 …
nonnegative or nonpositive integrable data, we prove the existence and uniqueness of mild …
The Kazdan–Warner equation on canonically compactifiable graphs
The Kazdan–Warner equation on canonically compactifiable graphs | SpringerLink Skip to
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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 …
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 …
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 …
2023 UNIQUENESS IN WEIGHTED lp SPACES FOR THE SCHRODINGER EQUATION ON …
Blow-up and global existence for semilinear parabolic equations on infinite graphs
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 …
semilinear heat equation posed on infinite graphs. The source term is a general function $ f …
General Cheeger inequalities for p-Laplacians on graphs
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 …
Unlike in previous works, we do not impose boundedness of the vertex degree, nor do we …
The wave equation on lattices and oscillatory integrals
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 …
lattice $\mathbb {Z}^ d $ with dimension $ d= 4$. Combining the singularity theory with …