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Nagumo type existence results for second-order nonlinear dynamic BVPS. (English) Zbl 1072.34015
A time scale ${\Bbb T}$ is a nonempty closed subset of ${\Bbb R}$. This paper studies the second-order nonlinear dynamic equation $y^{\Delta\Delta}(t)=f(t,y^\sigma(t),y^\Delta(t))$ on time scales with certain functional boundary conditions. The authors introduce a Nagumo-type condition (restricting the growth of $f$ in $y^\Delta$) and establish the existence of at least one solution of the given boundary value problem lying between the associated lower and upper solutions. An example is presented illustrating the main result.

##### MSC:
 34B15 Nonlinear boundary value problems for ODE 39A12 Discrete version of topics in analysis
##### Keywords:
time scale; Nagumo condition; lower and upper solutions
Full Text:
##### References:
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