The paper proves existence of ground states for the planar nonlinear Schrödinger-Newton system with point interaction under sufficient conditions on p, α, β and mass c, and links critical points to standing waves.
Bound states of two-dimensional Schr\"{o}dinger-Newton equations
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abstract
We prove an existence and uniqueness result for ground states and for purely angular excitations of two-dimensional Schr\"{o}dinger-Newton equations. From the minimization problem for ground states we obtain a sharp version of a logarithmic Hardy-Littlewood-Sobolev type inequality.
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2025 1verdicts
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Ground states of the planar nonlinear Schr\"odinger--Newton system with a point interaction
The paper proves existence of ground states for the planar nonlinear Schrödinger-Newton system with point interaction under sufficient conditions on p, α, β and mass c, and links critical points to standing waves.