2023/01/11 by Zubelevich, Oleg
#06A06 #34A12 #34A34 #34A36 #47H09 #47H10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2301.04437
We prove a fixed point theorem that combines the contraction mapping principle and some Knaster-Tarski-like theorem. As a consequence we obtain an existence theorem to initial value problem for ordinary differential equation with discontinuous vector field. This theorem generalizes Carathéodory's existence theorem.