Average value problems in ordinary differential equations (Q1958436)

The authors study existence and uniqueness results and the continuous dependence of the average condition for the functional value problem, which they called average value problem, \[ y'~=~F(x,y), \] \[ \int_{a}^{b}y(x)~d \nu~=~y_0, \] where \( \nu \) is any probability measure on \([a,b]\). The tools they use are Schauder's fixed point theorem and an integral representation given by \textit{S.-K. Chua} and \textit{R. L. Wheeden}, in [Indiana Univ. Math. J. 49, No.~1, 143--175 (2000; Zbl 0979.26009)].