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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.**
*(English)*
Zbl 1266.34144

Summary: We study a system of second-order dynamic equations on time scales \((p_1u^\nabla_1)^\Delta(t) - q_1(t)u_1(t) + \lambda f_1(t, u_1(t), u_2(t)) = 0\), \(t \in (t_1, t_n)\), \((p_2u^\nabla_2)^\Delta(t) - q_2(t)u_2(t) + \lambda f_2(t, u_1(t), u_2(t)) = 0\), 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.

### MSC:

34N05 | Dynamic equations on time scales or measure chains |

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\textit{G. Wu} et al., J. Appl. Math. 2013, Article ID 679316, 12 p. (2013; Zbl 1266.34144)

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