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• 作者：Dehong Ji
• 关键词：Positive solutions ; Four ; point boundary value problem ; \(p(t)\) ; Laplacian ; Fixed point index
• 刊名：Qualitative Theory of Dynamical Systems
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：15
• 期：1
• 页码：39-48
• 全文大小：408 KB
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• 作者单位：Dehong Ji (1)
  
  1. College of Science, Tianjin University of Technology, Tianjin, 300384, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Dynamical Systems and Ergodic Theory
  Difference and Functional Equations
  
• 出版者：Birkh盲user Basel
• ISSN：1662-3592

文摘

In this paper, by means of the computation of fixed point index, we obtain the existence of positive solutions for four-point boundary value problem involving the \(p(t)\)-Laplacian $$\begin{aligned}&(\phi (t,u'(t)))'+ f(t,u(t))=0,\quad t\in (0,1), \\&u'(0)=\alpha u'(\xi ),\quad u(1)=\beta u(\eta ), \end{aligned}$$where \(\phi (t,x)=|x|^{p(t)-2} \ x,\ p\in C([0,1],(1,+\infty )),\ \alpha ,\beta ,\xi ,\eta \in (0,1),\ \xi >\eta ,\ p(0)=p(\xi ),\ f\in C([0,1]\times [0,+\infty ),[0,+\infty ))\). Keywords Positive solutions Four-point boundary value problem \(p(t)\)-Laplacian Fixed point index Mathematics Subject Classification 34B16 34B18 This work is sponsored by the Tianjin City High School Science and Technology Fund Planning Project (No. (20141001)) and a project of Shandong province Higher Educational Science and Technology program (J11LA07).