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Existence of solitary waves for supercritical Schrödinger systems in dimension two

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Abstract

We prove existence of variational solutions for the Hamiltonian coupling of nonlinear Schrödinger equations in the whole plane, when the nonlinearities exhibit supercritical growth with respect to the Trudinger–Moser inequality. We discover linking type solutions which have finite energy in a suitable Lorentz–Sobolev space setting.

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Authors and Affiliations

  1. Dip. di Scienza e Alta Tecnologia, Università degli Studi dell’Insubria, via Valleggio 11, 22100, Como, Italy

    D. Cassani

  2. Dip. di Matematica “F. Enriques”, Università degli Studi di Milano, via C. Saldini 50, 20133, Milan, Italy

    C. Tarsi

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  1. D. Cassani
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  2. C. Tarsi
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Correspondence to D. Cassani.

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Communicated by A. Malchiodi.

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Cassani, D., Tarsi, C. Existence of solitary waves for supercritical Schrödinger systems in dimension two. Calc. Var. 54, 1673–1704 (2015). https://doi.org/10.1007/s00526-015-0840-3

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