LAUSR

Ground states of nonlinear Schrödinger equation on star metric graphs

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1 Published in 2018 at "Journal of Mathematical Analysis and Applications"

DOI: 10.1016/j.jmaa.2017.10.069

Abstract: Abstract The existence and nonexistence of the ground state to nonlinear Schrodinger equation on several types of metric graphs are considered. In particular, for some star graphs with only one central vertex, the existence of… read more here.

Keywords: graphs; metric graphs; ground states; equation ... See more keywords

On the eigenvalues for a weighted p-Laplacian operator on metric graphs

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1 Published in 2019 at "Complex Variables and Elliptic Equations"

DOI: 10.1080/17476933.2018.1434630

Abstract: ABSTRACTWe provide an explicit upper bound of the eigenvalues corresponding to a weighted p-Laplacian operator defined on a connected metric graph with finite total length. read more here.

Keywords: operator metric; laplacian operator; eigenvalues weighted; metric graphs ... See more keywords

Scattering on periodic metric graphs

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0 Published in 2020 at "Reviews in Mathematical Physics"

DOI: 10.1142/s0129055x20500245

Abstract: We consider the Laplacian on a periodic metric graph and obtain its decomposition into a direct fiber integral in terms of the corresponding discrete Laplacian. Eigenfunctions and eigenvalues of the fiber metric Laplacian are expressed… read more here.

Keywords: periodic metric; scattering periodic; metric graphs;

Approximations of Metric Graphs by Thick Graphs and Their Laplacians

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1 Published in 2019 at "Symmetry"

DOI: 10.3390/sym11030369

Abstract: The main purpose of this article is two-fold: first, to justify the choice of Kirchhoff vertex conditions on a metric graph as they appear naturally as a limit of Neumann Laplacians on a family of… read more here.

Keywords: graphs; approximations metric; thick graphs; metric graphs ... See more keywords

Nonlinear Schrödinger Equations on Periodic Metric Graphs

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0 Published in 2017 at "Discrete and Continuous Dynamical Systems"

DOI: 10.3934/dcds.2018030

Abstract: The paper is devoted to the nonlinear Schrodinger equation with periodic linear and nonlinear potentials on periodic metric graphs. Assuming that the spectrum of linear part does not contain zero, we prove the existence of… read more here.

Keywords: nonlinear schr; dinger equations; metric graphs; periodic metric ... See more keywords