Forward-backward bounded Filippov's solutions to nonsmooth ODE (Q2049358)

The paper studies second-order ordinary differential equations of the form \[ x''=f(t,x,x'), \] where \(f:\mathbb{R}\times M\times {\mathbb{R}}^m\to {\mathbb{R}}^m\) is a given mapping and \(M\subset {\mathbb{R}}^m\) is an open set. The mapping \(f\) is not continuous in the third variable. Under certain technical assumptions on the function \(f\) the existence of a generalized solution in the sense of Filippov for the equation above is proved.