$$\textrm{L}^{2}_{\alpha } $$ L α 2 -solutions for nonlinear Schrödinger equations associated with the Weinstein operator

Youssef Bettaibi ()
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Youssef Bettaibi: University of Gabes, Faculty of Sciences of Gabes, LR17ES11 Mathematics, Applications

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 1, 210-224

Abstract: Abstract In this article, we study the Schrödinger equation associated with the Weinstein operator (SW). We prove that the problem (SW) is locally well-posed in $$L_{\alpha }^{2}\left( \mathbb {R}^ {d+1}_+\right) $$ L α 2 R + d + 1 of the subcritical case $$p \in \left( 0, \frac{4}{d+2\alpha +2}\right] $$ p ∈ 0 , 4 d + 2 α + 2 and we show that the equation (SW) is globally well-posed in the critical case $$p=\frac{4}{d+2\alpha +2}$$ p = 4 d + 2 α + 2 .

Keywords: Schrödinger-Weinstein equations; Weinstein transform; Strichartz-type Schrödinger-Weinstein estimates; Dispersion phenomena; 35Q55; 42B35; 35Q41; 42B37; 42B10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-022-00356-0

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