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The two-point problem for nonlinear ordinary differential equations and differential inclusions. (English) Zbl 1002.34011
From the introduction: In the first part of this paper, the two-point Dirichlet problem $\ddot x(t)= f(t, x(t),\dot x(t)),\quad x(0)= x(T)= 0,\tag{$$*$$}$ for continuous functions $$f: [0,T]\times \mathbb{R}^{2n}\to \mathbb{R}^n$$ is considered. Assuming some additional conditions, the author proves the existence and uniqueness of solutions to $$(*)$$ and he compares the obtained theorems with earlier results. In the second part, an open problem for differential inclusions is formulated.

##### MSC:
 34B15 Nonlinear boundary value problems for ordinary differential equations 34A60 Ordinary differential inclusions