{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1362825896351857152.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"DOI","@value":"10.1142/s0219199701000494"}},{"identifier":{"@type":"URI","@value":"https://www.worldscientific.com/doi/pdf/10.1142/S0219199701000494"}}],"dc:title":[{"@value":"NONLINEAR SCHRÖDINGER EQUATIONS WITH STEEP POTENTIAL WELL"}],"description":[{"type":"abstract","notation":[{"@value":"<jats:p> We investigate nonlinear Schrödinger equations like the model equation [Formula: see text] where the potential V<jats:sub>λ</jats:sub> has a potential well with bottom independent of the parameter λ > 0. If λ → ∞ the infimum of the essential spectrum of -Δ + V<jats:sub>λ</jats:sub> in L<jats:sup>2</jats:sup>(ℝ<jats:sup>N</jats:sup>) converges towards ∞ and more and more eigenvalues appear below the essential spectrum. We show that as λ→∞ more and more solutions of the nonlinear Schrödinger equation exist. The solutions lie in H<jats:sup>1</jats:sup>(ℝ<jats:sup>N</jats:sup>) and are localized near the bottom of the potential well, but not near local minima of the potential. We also investigate the decay rate of the solutions as |x|→∞ as well as their behaviour as λ→∞. </jats:p>"}]}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1382825896351857153","@type":"Researcher","foaf:name":[{"@value":"THOMAS BARTSCH"}],"jpcoar:affiliationName":[{"@value":"Mathematisches Institut, Universität Giessen, Arndtstr. 2, 35392 Giessen, Germany"}]},{"@id":"https://cir.nii.ac.jp/crid/1382825896351857152","@type":"Researcher","foaf:name":[{"@value":"ALEXANDER PANKOV"}],"jpcoar:affiliationName":[{"@value":"Department of Mathematics, Vinnitsa State Pedagogical University, 287100 Vinnitsa, Ukraine"}]},{"@id":"https://cir.nii.ac.jp/crid/1382825896351857154","@type":"Researcher","foaf:name":[{"@value":"ZHI-QIANG WANG"}],"jpcoar:affiliationName":[{"@value":"Department of Mathematics and Statistics, Utah State University, Logan, UT 84322, USA"}]}],"publication":{"publicationIdentifier":[{"@type":"PISSN","@value":"02191997"},{"@type":"EISSN","@value":"17936683"}],"prism:publicationName":[{"@value":"Communications in Contemporary Mathematics"}],"dc:publisher":[{"@value":"World Scientific Pub Co Pte Lt"}],"prism:publicationDate":"2001-11","prism:volume":"03","prism:number":"04","prism:startingPage":"549","prism:endingPage":"569"},"reviewed":"false","url":[{"@id":"https://www.worldscientific.com/doi/pdf/10.1142/S0219199701000494"}],"createdAt":"2002-07-27","modifiedAt":"2019-08-06","relatedProduct":[{"@id":"https://cir.nii.ac.jp/crid/1360572092788364160","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Semi-classical states for logarithmic Schrödinger equations"}]}],"dataSourceIdentifier":[{"@type":"CROSSREF","@value":"10.1142/s0219199701000494"},{"@type":"CROSSREF","@value":"10.1088/1361-6544/abd52a_references_DOI_8GBSbXDtwx2Dw4WUcShC7LR6JIB"}]}