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Existence and multiplicity of positive solutions to nonlinear first-order PBVPs on time scales. (English) Zbl 1134.34016

Summary: We consider the following nonlinear first-order periodic boundary value problems on time scales
\[ \begin{cases} x^\Delta(t)+ p(t)x(\sigma(t))=f(x(t)), &t\in[0,T]_{\mathbb T},\\ x(0)=x(\sigma(T)). \end{cases} \]
Some new existence and multiplicity criteria of positive solutions are established by using several well-known fixed point theorems.

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
39A10 Additive difference equations
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