This paper is concerned with the existence of normalized solutions of the nonlinear Schrödinger equation (Formula presented.) in the mass supercritical and Sobolev subcritical case (Formula presented.) We prove the existence of a solution (Formula presented.) with prescribed L 2-norm (Formula presented.) under various conditions on the potential (Formula presented.) positive and vanishing at infinity, including potentials with singularities. The proof is based on a new min-max argument.
Normalized solutions of mass supercritical Schrödinger equations with potential
Verzini G.
2021-01-01
Abstract
This paper is concerned with the existence of normalized solutions of the nonlinear Schrödinger equation (Formula presented.) in the mass supercritical and Sobolev subcritical case (Formula presented.) We prove the existence of a solution (Formula presented.) with prescribed L 2-norm (Formula presented.) under various conditions on the potential (Formula presented.) positive and vanishing at infinity, including potentials with singularities. The proof is based on a new min-max argument.File in questo prodotto:
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