On the Cauchy problem for ordinary differential equations with discontinuous right-hand sides (Q2644815)

The authors are introducing the notion of ``angular continuity'' of \(f=f(t,x)\) and then they prove that this is sufficient for the existence of solutions of the Cauchy problem for \(x'(t)=f(t,x(t)).\) The angular continuity is strictly more general than the continuity and therefore their results extend some well-known results, including Peano's existence theorem.