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Positive solutions to singular semipositone boundary value problems of second order coupled differential systems

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Abstract

We establish the existence of positive solutions for the second order singular semipositone coupled Dirichlet systems

$$\left\{ \begin{aligned} &x{''} +f_1 \bigl(t,y(t)\bigr)+e_1(t)=0, \\ &y{''} +f_2\bigl(t,x(t) \bigr)+e_2(t)=0, \\ &x(0)=x(1)=0,\qquad y(0)=y(1)=0. \end{aligned} \right. $$

The proof relies on Schauder’s fixed point theorem.

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Authors and Affiliations

  1. Department of Applied Mathematics, Jilin University of Finance and Economics, Changchun, 130117, P.R. China

    Zhongwei Cao

  2. School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, P.R. China

    Zhongwei Cao & Daqing Jiang

  3. School of Mathematics, Jilin University, Changchun, 130012, P.R. China

    Yue Lv

  4. College of Science, Changchun University, Changchun, 130022, P.R. China

    Li Zu

Authors
  1. Zhongwei Cao
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  2. Yue Lv
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  3. Daqing Jiang
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  4. Li Zu
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Correspondence to Zhongwei Cao.

Additional information

The work was supported by Program for Changjiang Scholars and Innovative Research Team in University, NSFC of China (No.: 10971021), Science and Technology Research Project of Jilin Provincial Department of Education of China (No.: 2011176), Science and Technology Research Project of Jilin Provincial Department of Education of China (No.: 2010391), Youth Education Jun Projects of Jilin University of Finance and Economics.

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Cao, Z., Lv, Y., Jiang, D. et al. Positive solutions to singular semipositone boundary value problems of second order coupled differential systems. J. Appl. Math. Comput. 46, 1–16 (2014). https://doi.org/10.1007/s12190-013-0733-6

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  • DOI: https://doi.org/10.1007/s12190-013-0733-6

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