Electron. J. Diff. Eqns., Vol. 2005(2005), No. 17, pp. 1-14.

Positive solutions to a generalized second-order three-point boundary-value problem on time scales

Hua Luo, Qiaozhen Ma

Abstract:
Let $\mathbb{T}$ be a time scale with $0,T \in \mathbb{T}$. We investigate the existence and multiplicity of positive solutions to the nonlinear second-order three-point boundary-value problem
$$\displaylines{ u^{\Delta\nabla}(t)+a(t)f(u(t))=0,\quad t\in[0, T]\subset \mathbb{T},\cr u(0)=\beta u(\eta),\quad u(T)=\alpha u(\eta) }$$
on time scales $\mathbb{T}$, where 0, 0less than $\alpha$ less than $\frac{T}{\eta}$, 0 less than $\beta$ less than $\frac{T-\alpha\eta}{T-\eta}$ are given constants.

Submitted September 1, 2004. Published February 1, 2005.
Math Subject Classifications: 34B18, 39A10.
Key Words: Time scales; three-point boundary value problems; cone; fixed points; positive solutions.

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Hua Luo
College of Mathematics and Information Science
Northwest Normal University
Lanzhou 730070, Gansu, China
email: luohua@nwnu.edu.cn
Qiaozhen Ma
College of Mathematics and Information Science
Northwest Normal University
Lanzhou 730070, Gansu, China
email: maqzh@nwnu.edu.cn

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