Stable standing waves of nonlinear fractional Schrödinger equations

Li, Zaizheng; Zhang, Qidi; Zhang, Zhitao

doi:10.3934/cpaa.2022137

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2023

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“…The authors of this article [29] have already showed that there exists α 0,∞ ∈ [0, ∞] uniquely determined by N, s and f such that…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Standing Waves of Fractional Schrödinger Equations with Potentials and General Nonlinearities

Li,

null,

Zhang

2023

ATA

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We study the existence of standing waves of fractional Schr ödinger equations with a potential term and a general nonlinear term:where s ∈ (0, 1), N > 2s is an integer and V(x) ≤ 0 is radial. More precisely, we investigate the minimizing problem with L 2 -constraint:Under general assumptions on the nonlinearity term f (u) and the potential term V(x), we prove that there exists a constant α 0 ≥ 0 such that E(α) can be achieved for all α > α 0 , and there is no global minimizer with respect to E(α) for all 0 < α < α 0 . Moreover, we propose some criteria determining α 0 = 0 or α 0 > 0.

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“…The authors of this article [29] have already showed that there exists α 0,∞ ∈ [0, ∞] uniquely determined by N, s and f such that…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Standing Waves of Fractional Schrödinger Equations with Potentials and General Nonlinearities

Li,

null,

Zhang

2023

ATA

View full text Add to dashboard Cite

show abstract

Stable standing waves of nonlinear fractional Schrödinger equations

Abstract: We study the existence and orbital stability of standing waves of nonlinear fractional Schrödinger equations with a general nonlinear termWe investigate the minimizing problem with L 2 -constraint:

Cited by 1 publication

References 44 publications

Standing Waves of Fractional Schrödinger Equations with Potentials and General Nonlinearities

Standing Waves of Fractional Schrödinger Equations with Potentials and General Nonlinearities

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