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Zbl 1154.34310
Chang, Yong-Kui; Li, Wan-Tong
Existence results for second-order dynamic inclusion with $m$-point boundary value conditions on time scales.
(English)
[J] Appl. Math. Lett. 20, No. 8, 885-891 (2007). ISSN 0893-9659

The authors investigate the existence of solutions of the $m$-point boundary problem for the second-order dynamic inclusion on a time scale $\Bbb{T}$ \aligned y^{\triangle\nabla}(t)\in F(y(t)),\qquad t\in[0,b]_{\Bbb{T}},\\ y^{\triangle}(0)=\sum_{i=1}^{m-2}a_{i}y^{\triangle}(\zeta_i), \quad y(b)=\sum_{i=1}^{m-2}b_{i}y(\zeta_i). \endaligned They use a fixed point theorem of Sadovskii and a continuous selection theorem for lower semi-continuous multi-valued maps.
MSC 2000:
*34A60 ODE with multivalued right-hand sides
34B10 Multipoint boundary value problems
39A10 Difference equations

Keywords: Dynamic inclusions; Time scales; Boundary value; Fixed point; Lower semi-continuous multi-valued maps

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