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  • Positive solutions to the p...
    Cassani, Daniele; Du, Lele; Liu, Zhisu

    Nonlinear analysis, April 2024, 2024-04-00, Letnik: 241
    Journal Article

    In this paper we study the following nonlinear Choquard equation −Δu+u=ln1|x|∗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) 11.