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Positive Solutions for Four-Point Boundary Value Problem Involving the \(p(t)\)-Laplacian

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Abstract

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 \(\phi (t,x)=|x|^{p(t)-2} \ x,\ p\in C([0,1],(1,+\infty )),\ \alpha ,\beta ,\xi ,\eta \in (0,1),\ \xi >\eta ,\ p(0)=p(\xi ),\ f\in C([0,1]\times [0,+\infty ),[0,+\infty ))\).

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Authors and Affiliations

  1. College of Science, Tianjin University of Technology, Tianjin, 300384, China

    Dehong Ji

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  1. Dehong Ji
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Correspondence to Dehong Ji.

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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).

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Ji, D. Positive Solutions for Four-Point Boundary Value Problem Involving the \(p(t)\)-Laplacian. Qual. Theory Dyn. Syst. 15, 39–48 (2016). https://doi.org/10.1007/s12346-015-0139-y

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  • DOI: https://doi.org/10.1007/s12346-015-0139-y

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