## 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

#### Abstract

We study a system of second-order dynamic equations on time scales $\left({p}_{1}{u}_{1}^{\nabla }{\right)}^{\mathrm{\Delta }}\left(t\right)-{q}_{1}\left(t\right){u}_{1}\left(t\right)+\lambda {f}_{1}\left(t,{u}_{1}\left(t\right),{u}_{2}\left(t\right)\right)=0,t\in \left({t}_{1},{t}_{n}\right),\left({p}_{2}{u}_{2}^{\nabla }{\right)}^{\mathrm{\Delta }}\left(t\right)-{q}_{2}\left(t\right){u}_{2}\left(t\right)+\lambda {f}_{2}\left(t,{u}_{1}\left(t\right)$, ${u}_{2}\left(t\right)\right)=0$, satisfying four kinds of different multipoint boundary value conditions, ${f}_{i}$ is continuous and semipositone. We derive an interval of $\lambda$ such that any $\lambda$ 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

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