REVIEW 2 cited by
Fractional logarithmic Schr\"{o}dinger equations on lattice graphs
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
In this paper, we study the fractional logarithmic Schr\"{o}dinger equation $$ (-\Delta)^{s} u+h(x) u=u \log u^{2} $$ on lattice graphs $\mathbb{Z}^d$, where $s\in (0,1)$. If $h(x)$ is a bounded periodic potential, we prove the existence of ground state solution by mountain pass theorem and Lions lemma. If $h(x)$ is a coercive potential, we show the existence of ground state sign-changing solutions by the method of Nehari manifold.
Forward citations
Cited by 2 Pith papers
-
The Logarithmic Laplacian on General Graphs
The logarithmic Laplacian on weighted graphs is defined via a Bochner integral, given a kernel formula under stochastic completeness, and shown on Z^d to have sharp kernel bounds and exact diffusion asymptotics.
-
Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations
On the lattice Z^d, the discrete fractional logarithmic Kirchhoff equation admits a ground state for p>4, a ground state sign-changing solution for p>6, and at least four distinct weak solutions.
Discussion (0). Continue with ORCID to comment.