Existence of solutions to nonlinear differential equations with nonlocal conditions (Q1840812)

The authors consider the initial value problem for an abstract nonlinear ordinary differential equation of first order in some Banach space. The initial condition, which is a nonlocal condition, is of the type \(y(0)+ g(y)=y_0\), where \(g\) is some continuous function. Using a classical fixed-point theorem for compact maps due to Schäfer, the authors prove the existence of mild solutions.