$\mathrm{L}^{2}_{\alpha} $-Solutions for Nonlinear Schr\"odinger Equations Associated With The Weinstein Operator

Youssef Bettaibi

$\mathrm{L}^{2}_{\alpha} $-Solutions for Nonlinear Schr\"odinger Equations Associated With The Weinstein Operator

Analysis of PDEs 2021-11-30 v1

Authors: Youssef Bettaibi

Abstract

In this paper, we study the Schr\"odinger equation associated with the Weinstein operators and we prove the existence and uniqueness of global solutions to Schr\"odinger-Weinstein equations in\\ $C\left(\left(-T_{\min }, T_{\max }\right) ; L_{\alpha}^{2}\left(\mathbb{R}^{d+1}_+\right)\right) \bigcap L_{l o c}^{q_{1}}\left(\left(-T_{\min }, T_{\max }\right) ; L_{\alpha}^{r_{1}}\left(\mathbb{R}^{d+1}_+\right)\right)$ \\ on initial condition in $L_{\alpha}^{2}\left(\mathbb{R}^{d+1}_+\right)$

Keywords

nonlinear schrödinger equation nonlinear schrödinger equations nonlinear schrodinger equations

Cite

@article{arxiv.2111.14201,
  title  = {$\mathrm{L}^{2}_{\alpha} $-Solutions for Nonlinear Schr\"odinger Equations Associated With The Weinstein Operator},
  author = {Youssef Bettaibi},
  journal= {arXiv preprint arXiv:2111.14201},
  year   = {2021}
}

Comments

arXiv admin note: text overlap with arXiv:2101.04221

$\mathrm{L}^{2}_{\alpha} $-Solutions for Nonlinear Schr\"odinger Equations Associated With The Weinstein Operator

Abstract

Keywords

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