Bound states of two-dimensional Schrödinger-Newton equations

Abstract

We prove an existence and uniqueness result for ground states and for purely angular excitations of two-dimensional Schrödinger-Newton equations. From the minimization problem for ground states we obtain a sharp version of a logarithmic Hardy-Littlewood-Sobolev type inequality.

References in corpus (1)

• The one-dimensional Schrödinger-Newton equations

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• Bounds states of the Schrödinger-Newton model in low dimensions
• Existence and axial symmetry of minimal action odd solutions for 2-D Schrödinger-Newton equation
• On the existence and multiplicity of solutions for the $N$-Choquard logarithmic equation with exponential critical growth
• Symmetric Potentials Beget Symmetric Ground States