Abstract
In this paper we study the following nonlinear Choquard equation âÎu+u=ln1|x|âF(u)f(u),inR2,where fâC1(R,R) and F is the primitive of the nonlinearity f vanishing at zero. We use an asymptotic approximation approach to establish the existence of positive solutions to the above problem in the standard Sobolev space H1(R2). We give a new proof and at the same time extend part of the results established in (Cassani-Tarsi, Calc.Var.PDE, 2021) [11].
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