Spectral Analysis for a Singular Differential System with Integral Boundary Conditions

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• 作者：Fenglong Sun ; Lishan Liu ; Xinguang Zhang…
• 关键词：Mathematics Subject Classification34B16 ; 34B18 ; 34B40
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：13
• 期：6
• 页码：4763-4782
• 全文大小：607 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1660-5454
• 卷排序：13

文摘

In this paper, by constructing a cone K₁ × K₂ in the Cartesian product space C[0, 1] × C[0, 1], and using spectral analysis of the relevant linear operator for the corresponding differential system, some properties of the first eigenvalue corresponding to the relevant linear operator are obtained, and the fixed-point index of nonlinear operator in the K₁ × K₂ is calculated explicitly and the existence of at least one positive solution or two positive solutions of the singular differential system with integral boundary conditions is established.