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Twin positive solutions of nonlinear first-order boundary value problems on time scales. (English) Zbl 1139.34303
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:
34B15Nonlinear boundary value problems for ODE
39A10Additive difference equations
34B18Positive solutions of nonlinear boundary value problems for ODE
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References:
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