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Zbl 1122.34015
Boey, K.L.; Wong, Patricia J.Y.
Existence of triple positive solutions of two-point right focal boundary value problems on time scales. (English)
[J] Comput. Math. Appl. 50, No. 10-12, 1603-1620 (2005). ISSN 0898-1221

Summary: We consider the following boundary value problem, $$\alignat2 (-1)^{n-1}y^{\Delta n}(t) & =(-1)^{p+1}F(t,y(\sigma^{n-1}(t))), &\quad & t\in[a,b]\cap {\bold T},\\ y^{\Delta^i}(a)& =0, & \quad &0\le i\le p-1,\\ y^{\Delta^i}(\sigma(b))& =0, &\quad & p\le i\le n-1,\endalignat$$ where $n\le 2$, $1\le p \le n - 1$ is fixed and $\bold T$ 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 2000:: *34B18 Positive solutions of nonlinear boundary value problems
39A12 Discrete version of topics in analysis

Keywords: positive solutions; boundary value problems; two-point right focal boundary conditions; time scales

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