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Multiple Positive Solutions to Multipoint Boundary Value Problem for a System of Second‐Order Nonlinear Semipositone Differential Equations on Time Scales

Author

Listed:
  • Gang Wu
  • Longsuo Li
  • Xinrong Cong
  • Xiufeng Miao

Abstract

We study a system of second‐order dynamic equations on time scales (p1u1∇) Δ(t)-q1(t)u1(t)+λf1(t,u1(t),u2(t))=0,t∈(t1,tn),(p2u2∇) Δ(t)-q2(t)u2(t)+λf2(t,u1(t), u2(t)) = 0, satisfying four kinds of different multipoint boundary value conditions, fi is continuous and semipositone. We derive an interval of λ such that any λ lying in this interval, the semipositone coupled boundary value problem has multiple positive solutions. The arguments are based upon fixed‐point theorems in a cone.

Suggested Citation

  • Gang Wu & Longsuo Li & Xinrong Cong & Xiufeng Miao, 2013. "Multiple Positive Solutions to Multipoint Boundary Value Problem for a System of Second‐Order Nonlinear Semipositone Differential Equations on Time Scales," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:679316
    DOI: 10.1155/2013/679316
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    References listed on IDEAS

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    1. Chengjun Yuan & Yongming Liu, 2010. "Multiple Positive Solutions of a Second Order Nonlinear Semipositone m‐Point Boundary Value Problem on Time Scales," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    2. Chengjun Yuan & Yongming Liu, 2010. "Multiple Positive Solutions of a Second Order Nonlinear Semipositone -Point Boundary Value Problem on Time Scales," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-19, October.
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