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Zbl 1134.34016
Sun, Jian-Ping; Li, Wan-Tong
Existence and multiplicity of positive solutions to nonlinear first-order PBVPs on time scales.
(English)
[J] Comput. Math. Appl. 54, No. 6, 861-871 (2007). ISSN 0898-1221

Summary: We consider the following nonlinear first-order periodic boundary value problems on time scales $$\cases x^\Delta(t)+ p(t)x(\sigma(t))=f(x(t)), &t\in[0,T]_{\Bbb T},\\ x(0)=x(\sigma(T)). \endcases$$ Some new existence and multiplicity criteria of positive solutions are established by using several well-known fixed point theorems.
MSC 2000:
*34B18 Positive solutions of nonlinear boundary value problems
34B15 Nonlinear boundary value problems of ODE
39A10 Difference equations

Keywords: time scale; PBVP; positive solution; fixed point; existence and multiplicity

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