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On the Dirichlet problem for a second-order ordinary differential equation with discontinuous right-hand side. (English. Russian original) Zbl 1133.34309
Differ. Equ. 42, No. 3, 340-346 (2006); translation from Differ. Uravn. 42, No. 3, 320-326 (2006).
Consider the problem
\[ \begin{cases} x'' \in g(t,x,y)\\ x(0) = u,\quad x(T) = v,\quad u,v\in \mathbb{R}^{n}, \end{cases} \tag{1} \] where \(x:[0,T]\to \mathbb{R}^{n}, g:(a,b)\times \mathbb{R}^{n} \times \mathbb{R}^{n} \to \mathbb{R}^{n}\) is a given multifunction, \(a<0<T<b.\)
The paper is concerned with the existence of solutions of problem (1).

MSC:
34A60 Ordinary differential inclusions
34A36 Discontinuous ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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