Nontrivial solutions and least energy nodal solutions for a class of fourth-order elliptic equations

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• 作者：Guofeng Che ; Haibo Chen
• 关键词：Fourth ; order elliptic equations ; Nontrivial solutions ; Nodal solution ; Variational methods ; Nehari manifold
• 刊名：Journal of Applied Mathematics and Computing
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：53
• 期：1-2
• 页码：33-49
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Theory of Computation; Mathematics of Computing;
• 出版者：Springer Berlin Heidelberg
• ISSN：1865-2085
• 卷排序：53

文摘

This paper is concerned with the following fourth-order elliptic equation $$\begin{aligned} \left\{ \begin{array}{ll} \displaystyle \Delta ^{2}u-\Delta u+V(x)u=|u|^{p-1}u,\,\mathrm{in}\,\mathbb {R}^{N},\\ u\in H^{2}\left( \mathbb {R}^{N}\right) , \end{array} \right. \end{aligned}$$where \(p\in (2,\,2_{*}-1),\,u{\text {:}}\,\mathbb {R}^{N}\rightarrow \mathbb R.\) Under some appropriate assumptions on potential V(x),  the existence of nontrivial solutions and the least energy nodal solution are obtained by using variational methods.KeywordsFourth-order elliptic equationsNontrivial solutions Nodal solutionVariational methodsNehari manifoldMathematics Subject Classification35B3835J35References1.Lazer, A.C., McKenna, P.J.: Large-amplitude periodic oscillations in suspension bridges: some new connections with nonlinear analysis. 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Soc. 97(1), 48–62 (2014)MathSciNetCrossRefMATHGoogle ScholarCopyright information© Korean Society for Computational and Applied Mathematics 2015Authors and AffiliationsGuofeng Che1Haibo Chen1Email author1.School of Mathematics and StatisticsCentral South UniversityChangshaPeople’s Republic of China About this article CrossMark Publisher Name Springer Berlin Heidelberg Print ISSN 1598-5865 Online ISSN 1865-2085 About this journal Reprints and Permissions Article actions .buybox { margin: 16px 0 0; position: relative; } .buybox { font-family: Source Sans Pro, Helvetica, Arial, sans-serif; font-size: 14px; font-size: .875rem; } .buybox { zoom: 1; } .buybox:after, .buybox:before { content: ''; display: table; } .buybox:after { clear: both; } /*---------------------------------*/ .buybox .buybox__header { border: 1px solid #b3b3b3; border-bottom: 0; padding: 8px 12px; position: relative; background-color: #f2f2f2; } .buybox__header .buybox__login { font-family: Source Sans Pro, Helvetica, Arial, sans-serif; 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