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).
2024
2023
Asymptotic analysis; Concentration-compactness principle; Critical growth; Schrödinger-Poisson systems; Variational method
Cassani, D.; Du, L.; Liu, Z.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2166132
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