Normalized solutions for pseudo-relativistic Schrödinger equations
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Published:2024
Issue:1
Volume:16
Page:217-236
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ISSN:2836-3310
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Container-title:Communications in Analysis and Mechanics
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language:
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Short-container-title:CAM
Author:
Sun Xueqi1, Fu Yongqiang1, Liang Sihua2
Affiliation:
1. College of Mathematics, Harbin Institute of Technology, Harbin, 150001, P.R. China 2. College of Mathematics, Changchun Normal University, Changchun, 130032, P.R. China
Abstract
<abstract><p>In this paper, we consider the existence and multiplicity of normalized solutions to the following pseudo-relativistic Schrödinger equations</p>
<p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \left\{ \begin{array}{lll} \sqrt{-\Delta+m^2}u +\lambda u = \vartheta |u|^{p-2}v +|u|^{2^\sharp-2}v, & x\in \mathbb{R}^N, \ u>0, \\ \ \int_{{\mathbb{R}^N}}|u|^2dx = a^2, \end{array} \right. \end{equation*} $\end{document} </tex-math></disp-formula></p>
<p>where $ N\geq2, $ $ a, \vartheta, m > 0, $ $ \lambda $ is a real Lagrange parameter, $ 2 < p < 2^\sharp = \frac{2N}{N-1} $ and $ 2^\sharp $ is the critical Sobolev exponent. The operator $ \sqrt{-\Delta+m^2} $ is the fractional relativistic Schrödinger operator. Under appropriate assumptions, with the aid of truncation technique, concentration-compactness principle and genus theory, we show the existence and the multiplicity of normalized solutions for the above problem.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference39 articles.
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