We study the following Choquard type equation in the whole plane (C)-Δu+V(x)u=(I2∗F(x,u))f(x,u),x∈R2where I2 is the Newton logarithmic kernel, V is a bounded Schrödinger potential and the nonlinearity f(x, u), whose primitive in u vanishing at zero is F(x, u), exhibits the highest possible growth which is of exponential type. The competition between the logarithmic kernel and the exponential nonlinearity demands for new tools. A proper function space setting is provided by a new weighted version of the Pohozaev–Trudinger inequality which enables us to prove the existence of variational, in particular finite energy solutions to (C).
Schrödinger–Newton equations in dimension two via a Pohozaev–Trudinger log-weighted inequality / D. Cassani, C. Tarsi. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 60:5(2021 Oct), pp. 197.1-197.31. [10.1007/s00526-021-02071-w]
Schrödinger–Newton equations in dimension two via a Pohozaev–Trudinger log-weighted inequality
C. TarsiUltimo
2021
Abstract
We study the following Choquard type equation in the whole plane (C)-Δu+V(x)u=(I2∗F(x,u))f(x,u),x∈R2where I2 is the Newton logarithmic kernel, V is a bounded Schrödinger potential and the nonlinearity f(x, u), whose primitive in u vanishing at zero is F(x, u), exhibits the highest possible growth which is of exponential type. The competition between the logarithmic kernel and the exponential nonlinearity demands for new tools. A proper function space setting is provided by a new weighted version of the Pohozaev–Trudinger inequality which enables us to prove the existence of variational, in particular finite energy solutions to (C).File | Dimensione | Formato | |
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