A Dirichlet problem on the half-line for nonlinear equations with indefinite weight

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• 作者：Zuzana Došlá ; Mauro Marini ; Serena Matucci
• 关键词：Second ; order nonlinear differential equation ; Boundary value problem on the half ; line ; Dirichlet conditions ; Globally positive solution ; Disconjugacy ; Principal solution
• 刊名：Annali di Matematica Pura ed Applicata (1923 -)
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：196
• 期：1
• 页码：51-64
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer Berlin Heidelberg
• ISSN：1618-1891
• 卷排序：196

文摘

We study the existence of positive solutions on the half-line \([0,\infty )\) for the nonlinear second-order differential equation $$\begin{aligned} \bigl (a(t)x^{\prime }\bigr )^{\prime }+b(t)F(x)=0,\quad t \ge 0, \end{aligned}$$satisfying Dirichlet-type conditions, say \(x(0)=0\), \(\lim _{t\rightarrow \infty }x(t)=0\). The function b is allowed to change sign, and the nonlinearity F is assumed to be asymptotically linear in a neighborhood of zero and infinity. Our results cover also the cases in which b is a periodic function for large t or it is unbounded from below.KeywordsSecond-order nonlinear differential equationBoundary value problem on the half-lineDirichlet conditionsGlobally positive solutionDisconjugacyPrincipal solutionMathematics Subject ClassificationPrimary 34B40Secondary 34B18References1.Agarwal, R.P., O’Regan, D.: Infinite Interval Problems for Differential, Difference and Integral Equations. 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Value Probl. 2013, 141 (2013)MathSciNetCrossRefMATHGoogle ScholarCopyright information© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg 2016Authors and AffiliationsZuzana Došlá1Email authorMauro Marini2Serena Matucci21.Department of Mathematics and StatisticsMasaryk UniversityBrnoCzech Republic2.Department of Mathematics and Informatics “Ulisse Dini”University of FlorenceFlorenceItaly About this article CrossMark Publisher Name Springer Berlin Heidelberg Print ISSN 0373-3114 Online ISSN 1618-1891 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; 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