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Sun, Jian-Ping; Li, Wan-Tong

Existence of solutions to nonlinear first-order PBVPs on time scales. (English) Zbl 1120.34314

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 67, No. 3, 883-888 (2007).
Summary: We are concerned with the following nonlinear first-order periodic boundary value problem on time scales \[ \begin{cases} x^\Delta(t)+p(t)x (\sigma(t))=g(t,x(\sigma (t))),\;t\in[0,T]_\mathbb{T},\\ x(0)=x(\sigma(T)). \end{cases} \] Some new existence criteria of at least one solution are established by using new inequalities and the well-known Schaefer fixed-point theorem.

Cited in 14 Documents

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
39A10 Additive difference equations

Keywords:

time scale; periodic boundary value problems; solution; fixed point
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\textit{J.-P. Sun} and \textit{W.-T. Li}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 67, No. 3, 883--888 (2007; Zbl 1120.34314)
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References:

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