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On the solution set of a nonconvex nonclosed second order differential inclusion. (English) Zbl 1133.34009

The paper concerns the system which consists of the second order differential inclusion
\[ x''(t)\in F(t,x(t),H(t,x(t)) \]
and the boundary conditions
\[ x(0)-k_1x'(0)=c_1,\quad x(1)+k_2x'(1)=c_2. \]
Here, the scalar multifunctions \(F\) and \(H\) are at least closed valued. Although the multifunction \((t,u)\to F(t,u,H(t,u))\) is not necessarily closed valued [cf. A. Belarbi and M. Benchohra, Electron. J. Differ. Equ. 2005, Paper No. 06 (2005; Zbl 1075.34015)], the solution multifunction \((c_1,c_2)\to S(c_1,c_2)\) has some meaningful properties.

MSC:

34A60 Ordinary differential inclusions
47H10 Fixed-point theorems

Citations:

Zbl 1075.34015
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