Existence of solutions of first-order differential equations via a fixed point theorem for discontinuous operators - Sestelo, Rubén Figueroa; Pouso, Rodrigo López (Fixed point theory and algorithms for sciences and engineering, 2015)
We use a recent Schauder-type result for discontinuous operators in order to look for solutions for first-order differential equations subject to initial functional conditions. We show how this abstract fixed-point result allows us to consider a nonlinearity which can be strongly discontinuous. Some examples of applications and comparison with recent literature are included.