Journal of Applied Mathematics

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

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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.

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 679316, 12 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394807910

Digital Object Identifier
doi:10.1155/2013/679316

Mathematical Reviews number (MathSciNet)
MR3039716

Zentralblatt MATH identifier
1266.34144

Citation

Wu, Gang; Li, Longsuo; Cong, Xinrong; Miao, Xiufeng. Multiple Positive Solutions to Multipoint Boundary Value Problem for a System of Second-Order Nonlinear Semipositone Differential Equations on Time Scales. J. Appl. Math. 2013 (2013), Article ID 679316, 12 pages. doi:10.1155/2013/679316. https://projecteuclid.org/euclid.jam/1394807910


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