Solutions on Asymptotically Periodic Elliptic System with New Conditions

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• 作者：Dongdong Qin ; Xianhua Tang
• 关键词：Elliptic system ; superlinear ; asymptotically periodic ; ground state ; strongly indefinite functionals
• 刊名：Results in Mathematics
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：70
• 期：3-4
• 页码：539-565
• 全文大小：743 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-9012
• 卷排序：70

文摘

This paper is concerned with the following elliptic system:$$\left\{\begin{array}{l@{\quad}l@{\quad}l}-\Delta u+U_{1}(x)u =F_{u}(x,u,v)&\mbox{in}&\mathbb{R}^{N},\\ -\Delta v+U_{2}(x)v=F_{v}(x,u,v)& \mbox{in}&\mathbb{R}^{N},\\ u, \ v \in H^{1}(\mathbb{R}^{N}).\end{array}\right.$$Assuming that the potential U_i(x) are periodic in x and 0 lies in a spectral gap of \({\sigma (-\Delta + U_{i}), i=1,2}\), two types of ground state solutions are obtained with some new super-quadratic conditions on nonlinearity F which are weaker that some well known ones. For the case that U_i(x) and F(x,u,v) are asymptotically periodic in x, a nontrivial solution is established by using a generalized linking theorem and some new techniques.KeywordsElliptic systemsuperlinearasymptotically periodicground statestrongly indefinite functionalsMathematics Subject Classification35J2035J50References1.Bartsch T., Clapp M.: Critical point theory for indefinite functionals with symmetries. J. Funct. 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Math. 104, 343–358 (2001)MathSciNetCrossRefMATHGoogle ScholarCopyright information© Springer Basel 2015Authors and AffiliationsDongdong Qin1Email authorXianhua Tang11.School of Mathematics and StatisticsCentral South UniversityChangshaPeople’s Republic of China About this article CrossMark Print ISSN 1422-6383 Online ISSN 1420-9012 Publisher Name Springer International Publishing About this journal Reprints and Permissions Article actions function trackAddToCart() { var buyBoxPixel = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox", product: "10.1007/s00025-015-0491-x_Solutions on Asymptotically Period", productStatus: "add", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); buyBoxPixel.sendinfo(); } function trackSubscription() { var subscription = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox" }); subscription.sendinfo({linkId: "inst. subscription info"}); } window.addEventListener("load", function(event) { var viewPage = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "SL-article", product: "10.1007/s00025-015-0491-x_Solutions on Asymptotically Period", productStatus: "view", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); viewPage.sendinfo(); }); Log in to check your access to this article Buy (PDF)EUR 34,95 Unlimited access to full article Instant download (PDF) Price includes local sales tax if applicable Find out about institutional subscriptions Export citation .RIS Papers Reference Manager RefWorks Zotero .ENW EndNote .BIB BibTeX JabRef Mendeley Share article Email Facebook Twitter LinkedIn Cookies We use cookies to improve your experience with our site. 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