Monotone iterative technique for first-order nonlinear periodic boundary value problems on time scales. (English) Zbl 1207.34080

Zhao, Ya-Hong; Sun, Jian-Ping

Adv. Difference Equ. 2010, Article ID 620459, 10 p. (2010).

Summary: We investigate the following nonlinear first-order periodic boundary value problem on time scales:
\[ x^{\Delta }(t)+p(t)x(\sigma (t))=f(t,x(t)),\quad t\in [_{0,T]_{T}},\;x(0)=x(\sigma (T)). \]
Some new existence criteria for positive solutions are established by using the monotone iterative technique.

MSC:

34K10	Boundary value problems for functional-differential equations
34N05	Dynamic equations on time scales or measure chains
34K07	Theoretical approximation of solutions to functional-differential equations

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