{"title":"Multiple Normalized Solutions for Nonlinear Biharmonic Schrödinger Equations in ℝN with L2-Subcritical Growth","authors":"Jun Wang, Li Wang, Ji-xiu Wang","doi":"10.1007/s10255-024-1131-6","DOIUrl":null,"url":null,"abstract":"<p>In this article, we consider the existence of normalized solutions for the following nonlinear biharmonic Schrödinger equations</p><span>$$\\left\\{{\\matrix{{{\\Delta ^2}u = \\lambda u + h\\left({\\varepsilon x} \\right)\\,f\\left(u \\right),} & {x \\in \\mathbb{R}{^N},} \\cr {\\int_{\\mathbb{R}{^N}} {{{\\left| u \\right|}^2}dx = {c^2},}} & {x \\in \\mathbb{R}{^N},} \\cr}} \\right.$$</span><p>where <i>c, ε</i> > 0; <i>N</i> ≥ 5; <i>λ</i> ∈ ℝ is a Lagrange multiplier and is unknown, <i>h</i> ∈ <i>C</i>(ℝ<sup><i>N</i></sup>; [0;∞)); <i>f</i>: ℝ → ℝ is continuous function satisfying <i>L</i><sup>2</sup>-subcritical growth. When <i>ε</i> is small enough, we get multiple normalized solutions. Moreover, we also obtain orbital stability of the solutions.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10255-024-1131-6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, we consider the existence of normalized solutions for the following nonlinear biharmonic Schrödinger equations
where c, ε > 0; N ≥ 5; λ ∈ ℝ is a Lagrange multiplier and is unknown, h ∈ C(ℝN; [0;∞)); f: ℝ → ℝ is continuous function satisfying L2-subcritical growth. When ε is small enough, we get multiple normalized solutions. Moreover, we also obtain orbital stability of the solutions.