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

Gang Wu, Longsuo Li, Xinrong Cong and Xiufeng Miao

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

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.

Date: 2013
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https://doi.org/10.1155/2013/679316

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:679316

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