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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.

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