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- W3023643048 abstract "In this paper, we study existence of a standing wave solution for the nonlinear Schrödinger equation with a real-valued linear potential in energy-subcritical. Moreover, we also prove global well-posedness to the Cauchy problem with the initial data, whose action is less than that of the ground state with the potential. Hong [Commun. Pure Appl. Anal. 15 (2016), pp. 1571â1601] and the authors showed a scattering result for the problem with the initial data, whose action is less than that of the ground state without the potential. It was noted that the action of the ground state with the potential is greater than that of the ground state without the potential. Our new contribution enables us to treat initial data, which were not treated in those papers." @default.
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- W3023643048 date "2020-09-17" @default.
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- W3023643048 title "Global well-posedness below the ground state for the nonlinear Schrödinger equation with a linear potential" @default.
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- W3023643048 doi "https://doi.org/10.1090/proc/15161" @default.
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