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Zbl 1139.34303
Sun, Jian-Ping
Twin positive solutions of nonlinear first-order boundary value problems on time scales.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 68, No. 6, A, 1754-1758 (2008). ISSN 0362-546X

Summary: We consider the following nonlinear first-order boundary value problem on time scale $\Bbb T$ $$\cases x^\Delta(t)=f(x(\sigma(t))), & t\in [0,T]_{\Bbb T},\\ x(0)=\beta x(\sigma(T)),\endcases$$ where $0<\beta<1$. Some existence criteria for at least two positive solutions are established by using the well-known twin-fixed-point theorem due to Avery and Henderson.
MSC 2000:
*34B15 Nonlinear boundary value problems of ODE
39A10 Difference equations
34B18 Positive solutions of nonlinear boundary value problems

Keywords: positive solution; fixed point

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