Boundary value problems with discontinuities in the spatial variable (Q1900656)

Under the assumption that \(f = f(t,x)\), \(x \in R^n\) is measurable, but not necessarily continuous, and using Filippov's theory, the problem (1) \(x' = f(t,x)\), \(x(0) = x(1)\) is reformulated as a differential inclusion and then the existence principles proved by \textit{A. Granas}, \textit{R. B. Guenther} and \textit{L. W. Lee} [C. R. Acad. Sci., Paris, Ser. I 307, No. 8, 391-396 (1988; Zbl 0652.34018)] are applied to prove the existence of a solution to (1).