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Soliton solutions for a quasilinear Schrödinger equation with critical exponent

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  • This paper is concerned with the existence of soliton solutions for a quasilinear Schrödinger equation in $R^N$ with critical exponent, which appears from modelling the self-channeling of a high-power ultrashort laser in matter. By working with a perturbation approach which was initially proposed in [26], we prove that the given problem has a positive ground state solution.
    Mathematics Subject Classification: Primary: 35J62; Secondary: 35B09, 35B33.

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