In this paper we study the following nonlinear Choquard equation −Δu+u=ln[Formula presented]∗F(u)f(u),inR2,where f∈C1(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).
Positive solutions to the planar logarithmic Choquard equation with exponential nonlinearity
Cassani D.
;Du L.;Liu Z.
2024-01-01
Abstract
In this paper we study the following nonlinear Choquard equation −Δu+u=ln[Formula presented]∗F(u)f(u),inR2,where f∈C1(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).
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