Ground-State Solutions for Asymptotically Cubic Schrödinger–Maxwell Equations
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In this paper, using variational methods and critical point theory, we study the existence of ground-state solutions for the following nonlinear Schrödinger–Maxwell equations$$\left\{\begin{array}{l@{\quad}l} -\triangle u + V(x)u + \phi u = f(x, u), & {\rm in}\, \mathbb{R}^{3},\\ -\triangle\phi = 4\pi u^{2}, & {\rm in} \, \mathbb{R}^{3},\end{array}\right. $$ (NSM)where f is asymptotically cubic, V 1-periodic in each of \({x_1, x_2, x_3}\) and \({\underline{V}:= {\rm inf}_{x\in\mathbb{R}^3}V(x) > 0}\). Under some more assumptions on V and f, we develop a direct and simple method to find ground-state solutions for \({(\mathrm{NSM})}\). The main idea is to find a minimizing (PS) sequence for the energy functional outside the Nehari manifold \({\mathcal{N}}\) using the diagonal method. 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Math. 104, 343–358 (2001)MathSciNetMATHCrossRefGoogle ScholarCopyright information© Springer International Publishing 2016Authors and AffiliationsWen-nian Huang1Email authorX. H. Tang21.School of Mathematics and StatisticsGuangxi Normal UniversityGuilinPeople’s Republic of China2.School of Mathematics and StatisticsCentral South UniversityChangshaPeople’s Republic of China About this article CrossMark Print ISSN 1660-5446 Online ISSN 1660-5454 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/s00009-016-0697-5_Ground-State Solutions for Asympto", 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/s00009-016-0697-5_Ground-State Solutions for Asympto", 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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