Infinitely many sign-changing solutions for the nonlinear Schrödinger-Poisson system with super 2-linear growth at infinity

Infinitely many sign-changing solutions for the nonlinear Schrödinger-Poisson system with super 2-linear growth at infinity | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Infinitely many sign-changing solutions for the nonlinear Schrödinger-Poisson system with super 2-linear growth at infinity Shuai Wang, Xing-Ping Wu, Chun-Lei Tang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2114666/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Note: Please see pdf for full abstract with equations. In this paper, we investigate the sign-changing solutions to the following Schrödinger-Poisson system −∆u + V (x)u + λφ(x)u = f (u), x ∈ R 3 , −∆φ = u 2 , x ∈ R 3 , where λ > 0 is a parameter and f is super 2-linear at infinity. By using the method of invariant sets of descending flow and a multiple critical points theorem, we prove that this system possesses infinitely many sign-changing solutions for any λ > 0. Mathematics Subject Classification. 35J20 · 35J60. Schrödinger-Poisson system Sign-changing solutions Super 2-linear Invariant sets of descending flow Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-2114666","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":140637948,"identity":"3215525a-4a30-4e96-bac1-3c1744a155af","order_by":0,"name":"Shuai Wang","email":"","orcid":"","institution":"Southwest University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Shuai","middleName":"","lastName":"Wang","suffix":""},{"id":140637949,"identity":"86c67fda-c6bb-42cc-8137-bf4836cf623c","order_by":1,"name":"Xing-Ping Wu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAApklEQVRIiWNgGAWjYLCCDxDKgHgdjDNI1sLMQ5IWgxs5Zo9t/hxObGBv3ibBUHOHGC1p6ca5bUAtPMfKJBiOPSOsxexG8jHp3IbbiQ0SOWYSjA2HidGS2CZt8QeoRf4N0VqAtjCwgWzhIVKL/Zln6Ya9bf+N23jSii0SjhGhRbI9x+zBjz9psv3shzfe+FBDhBYgYEOQCURpgGkZBaNgFIyCUYATAAAF4DjbzkpjbQAAAABJRU5ErkJggg==","orcid":"","institution":"Southwest University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Xing-Ping","middleName":"","lastName":"Wu","suffix":""},{"id":140637950,"identity":"986222f4-976c-478c-b120-f4bb4a498066","order_by":2,"name":"Chun-Lei Tang","email":"","orcid":"","institution":"Southwest University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Chun-Lei","middleName":"","lastName":"Tang","suffix":""}],"badges":[],"createdAt":"2022-09-29 03:29:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2114666/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2114666/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":27474610,"identity":"386c44fc-01ab-4f23-a641-858391b63fa9","added_by":"auto","created_at":"2022-10-07 15:15:32","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":352915,"visible":true,"origin":"","legend":"","description":"","filename":"Infinitelymanysignchangingsolutions.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2114666/v1_covered.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Infinitely many sign-changing solutions for the nonlinear Schrödinger-Poisson system with super 2-linear growth at infinity","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-2114666/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Schrödinger-Poisson system, Sign-changing solutions, Super 2-linear, Invariant sets of descending flow","lastPublishedDoi":"10.21203/rs.3.rs-2114666/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2114666/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eNote: Please see pdf for full abstract with equations.\u003c/p\u003e\n\u003cp\u003eIn this paper, we investigate the sign-changing solutions to the following Schrödinger-Poisson system\u003c/p\u003e\n\u003cp\u003e−∆u + V (x)u + λφ(x)u = f (u), x ∈ R\u003csup\u003e3\u003c/sup\u003e ,\u003c/p\u003e\n\u003cp\u003e−∆φ = u\u003csup\u003e2\u003c/sup\u003e , x ∈ R\u003csup\u003e3\u003c/sup\u003e ,\u003c/p\u003e\n\u003cp\u003ewhere λ \u0026gt; 0 is a parameter and f is super 2-linear at infinity. By using the method of invariant sets of descending flow and a multiple critical points theorem, we prove that this system possesses infinitely many sign-changing solutions for any λ \u0026gt; 0.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eMathematics Subject Classification. 35J20 · 35J60.\u003c/p\u003e","manuscriptTitle":"Infinitely many sign-changing solutions for the nonlinear Schrödinger-Poisson system with super 2-linear growth at infinity","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2022-10-07 15:15:17","doi":"10.21203/rs.3.rs-2114666/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"5af0ba9a-2c6a-4841-8305-7159a0f7b9fc","owner":[],"postedDate":"October 7th, 2022","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2022-12-08T11:29:41+00:00","versionOfRecord":[],"versionCreatedAt":"2022-10-07 15:15:17","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-2114666","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2114666","identity":"rs-2114666","version":["v1"]},"buildId":"7rjqhiLT3MXkJMwkYKINL","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}