Existence and multiplicity of positive solutions to nonlinear Schrödinger equations on a bridge type unbounded graph

Shi, Junping; Zhou, Jiazheng

doi:10.1090/proc/17213

Existence and multiplicity of positive solutions to nonlinear Schrödinger equations on a bridge type unbounded graph
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by Junping Shi and Jiazheng Zhou;

Proc. Amer. Math. Soc.

DOI: https://doi.org/10.1090/proc/17213

Published electronically: June 27, 2025

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Abstract:

The existence of positive standing wave solutions to a nonlinear Schrödinger equation on a bridge type unbounded metric graph (a domain of multiple half-lines with two junctions connected by a line segment with arbitrary length) is showed, and under certain conditions, the existence of multiple positive solutions is proved. Similar results also hold for the equation with bistable nonlinearity.

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Existence and multiplicity of positive solutions to nonlinear Schrödinger equations on a bridge type unbounded graph
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Abstract: