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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
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