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Multiple positive solutions for time scale boundary value problems on infinite intervals

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An Erratum to this article was published on 17 December 2009

Abstract

The study of dynamic equations on time scales is an area of mathematics. It has been created in order to unify the study of differential and difference equations. In this paper, we consider the time-scale boundary value problems

$$\left\{\begin{array}{l@{\quad }l}(\phi_{p}(u^{\triangle}(t)))^{\nabla}+q(t)f(u(t),u^{\triangle}(t))=0,&t\in(0,\infty)_{\mathbb{T}},\\[3pt]u(0)=\beta u^{\triangle}(\eta),\quad \lim\limits_{t\in\mathbb{T},t\rightarrow\infty}u^{\triangle}(t)=0,\end{array}\right.$$

where \(\mathbb{T}\) is a time scale. By means of Leggett-Williams fixed point theorem, sufficient conditions are obtained that guarantee the existence of at least three positive solutions to the above boundary value problem. The results obtained are even new for the special cases of difference dynamic equations (when \(\mathbb{T}=\mathbb{Z}\) ) and differential dynamic equations (when \(\mathbb{T}=\mathbb{R}\) ), as well as in the general time scale setting.

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Authors and Affiliations

  1. Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China

    Xiangkui Zhao & Weigao Ge

  2. Applied Science School, University of Science and Technology Beijing, Beijing, 100083, People’s Republic of China

    Xiangkui Zhao

Authors
  1. Xiangkui Zhao
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  2. Weigao Ge
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Corresponding author

Correspondence to Xiangkui Zhao.

Additional information

Supported by National Natural Sciences Foundation of China (10671012) and the Doctoral Program Foundation of Education Ministry of China (20050007011).

An erratum to this article can be found at http://dx.doi.org/10.1007/s10440-009-9557-7

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Zhao, X., Ge, W. Multiple positive solutions for time scale boundary value problems on infinite intervals. Acta Appl Math 106, 265–273 (2009). https://doi.org/10.1007/s10440-008-9294-3

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  • DOI: https://doi.org/10.1007/s10440-008-9294-3

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