Another look at planar Schrödinger-Newton systems
Zhisu Liu, Vicenţiu D. Rădulescu, Chun‐Lei Tang, Jianjun Zhang
Abstract
In this paper, we focus on the existence of positive solutions to the following planar Schrödinger-Newton system with general subcritical growth{−Δu+u+ϕu=f(u)inR2,Δϕ=u2inR2, where f is a smooth reaction. We introduce a new variational approach, which enables us to study the above problem in the Sobolev space H1(R2). The analysis developed in this paper also allows to investigate the relationship between a Schrödinger-Newton system of Riesz-type and a Schrödinger-Newton system of logarithmic-type. Furthermore, this new approach can provide a new look at the planar Schrödinger-Newton system and may it have some potential applications in various related problems.
Topics & Concepts
PlanarMathematicsSobolev spaceSchrödinger's catFocus (optics)Newton's methodSpace (punctuation)Applied mathematicsMathematical analysisPhysicsComputer scienceNonlinear systemQuantum mechanicsOpticsComputer graphics (images)Operating systemNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringNonlinear Differential Equations Analysis