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Existence of triple positive solutions of two-point right focal boundary value problems on time scales. (English) Zbl 1122.34015
Summary: We consider the following boundary value problem,
\begin{alignedat}{2} (-1)^{n-1}y^{\Delta n}(t) & =(-1)^{p+1}F(t,y(\sigma^{n-1}(t))), &\quad & t\in[a,b]\cap {\mathbf T},\\ y^{\Delta^i}(a)& =0, & \quad &0\leq i\leq p-1,\\ y^{\Delta^i}(\sigma(b))& =0, &\quad & p\leq i\leq n-1,\end{alignedat} where $$n\leq 2$$, $$1\leq p \leq n - 1$$ is fixed and $$\mathbf T$$ is a time scale. By applying fixed-point theorems for operators on a cone, existence criteria are developed for triple positive solutions of the boundary value problem. We also include examples to illustrate the usefulness of the results obtained.

##### MSC:
 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 39A12 Discrete version of topics in analysis
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##### References:
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